*1 Before R IPPLE , R OVNER , and S YKES , Circuit Judges . S YKES , Circuit Judge . For nearly a decade, John Gries and James McCullars were active participants in a private online chat room frequented by pedophiles sharing large volumes of child pornography. They were indicted for conspiracy to distribute child pornography, conspiracy to sexually exploit *2 a child, and engaging in a child-exploitation enterprise. Other users of the chat room cooperated with investigators, pleaded guilty, and received sentencing consideration. The charges against Gries and McCullars proceeded to trial; several cooperators testified against them.

To convict Gries and McCullars of the enterprise offense, the government had to prove that they committed three or more crimes against children “in concert” with three or more persons. 18 U.S.C. § 2252A(g)(2). The jury found them guilty on all charges.

At sentencing the parties and the judge overlooked an important point: The conspiracy counts are lesser-included offenses of the enterprise count. Instead of merging those convictions and imposing sentence on the greater offense or lesser offenses alone, the judge imposed concurrent sentenc- es on all three convictions. That error violates the Double Jeopardy Clause. Rutledge v. United States , 517 U.S. 292, 307 (1996). We reverse and remand with instructions to vacate the sentences on either the greater or lesser counts and enter new judgments accordingly. The remaining issues on appeal are meritless.

I. Background

For almost ten years, Gries and McCullars participated in an online conspiracy of pedophiles who shared large collec- tions of child pornography and discussed the sexual exploi- tation of children. The group used password-protected chat rooms to privately communicate in real time and facilitate the exchange of massive personal libraries of child pornog- raphy. Collectively, the libraries contained thousands of files containing images depicting the violent sexual abuse of *3 thousands of children. The files were encrypted, but mem- bers of the group shared passwords to give chat-room participants access to the contents. When a group member had new material to share, he would message others in the chat room, describe the contents of the file, and offer it for distribution.

Investigators estimated that at its peak the conspiracy in- cluded as many as 35 to 40 participants, but the government could identify only Gries, McCullars, and 11 other cocon- spirators. Most cooperated with investigators by handing over and decrypting their child-pornography collections. Gries also did so, but McCullars did not. Nine coconspira- tors pleaded guilty to a single count of engaging in a child- exploitation enterprise in violation of § 2252A(g)(2); they are serving prison terms ranging from 135 to 360 months.

A grand jury indicted Gries and McCullars on three counts: conspiracy to distribute and receive child pornogra- phy, 18 U.S.C. § 2252A(a)(2); conspiracy to sexually exploit a child, 18 U.S.C. § 2251(d)(1)(A); and engaging in a child- exploitation enterprise, § 2252A(g)(2). Gries was also charged separately with five additional counts of receiving child pornography. Three of their coconspirators agreed to testify for the government in exchange for favorable sentenc- ing recommendations.

The charges against Gries and McCullars were tried to a jury over the course of a week. To convict them on the enterprise charge, the government had to prove beyond a reasonable doubt that each defendant committed at least three predicate crimes against children “in concert” with three other people. § 2252A(g)(2). The predicates included the conspiracies alleged in counts one and two, together *4 with multiple separate acts of distributing, receiving, and advertising child pornography.

The jury found the defendants guilty on all counts. On the enterprise count, the jury found that Gries committed 10 predicate offenses, including the conspiracies charged in counts one and two. The jury found that McCullars commit- ted 17 predicate crimes, including the two conspiracies.

Under the Sentencing Guidelines, Gries faced an adviso- ry imprisonment range of 324 to 405 months. The judge imposed a sentence of 240 months on count one (conspiracy to distribute child pornography), 360 months on count two (the child-exploitation conspiracy), 360 months on the enterprise count, and 240 months on each separate convic- tion for receiving child pornography. The terms are concur- rent, yielding an aggregate sentence of 360 months, the midpoint of the advisory range. The guidelines recommend- ed a life sentence for McCullars. The judge imposed a sen- tence of 240 months on count one, 360 months on count two, and life in prison on the enterprise count. Again these terms are running concurrently.

II. Discussion

Gries and McCullars raise three arguments on appeal. First, they contend that the separate sentences on the three counts of conviction violate the Double Jeopardy Clause because the conspiracies are predicates for, and thus lesser- included offenses of, the enterprise offense. Next, they argue that the government failed to prove an element of the con- spiracy charged in count two—namely, that they “noticed” or “advertised” child pornography for distribution or ex- *5 change. § 2251(d)(1)(A). Finally, they argue that their sen- tences are unreasonably long.

The defendants failed to preserve the first two argu- ments, so our review is governed by the plain-error stand- ard. Reversal is warranted only if a clear or obvious error in the proceedings below affected the defendants’ substantial rights and the fairness, integrity, or public reputation of the judicial process. United States v. Christian , 673 F.3d 702, 708 (7th Cir. 2012).

A. Double Jeopardy

The defendants first argue that the conspiracy counts are lesser-included offenses of the enterprise count, so imposing concurrent sentences on all three counts amounts to three separate punishments for the “same offense” in violation of the Fifth Amendment’s Double Jeopardy Clause. ^[1] We agree.

It is well understood that two statutory violations are considered to be the same offense for purposes of double jeopardy when “one is a lesser included offense of the other.” Rutledge , 517 U.S. at 297. The Supreme Court’s deci- sion in Rutledge is directly applicable to the double-jeopardy question presented here, though everyone apparently missed it in the district court. In Rutledge the defendant was charged with conspiracy to distribute controlled substances in violation of 21 U.S.C. § 846 and a coterminous continuing criminal enterprise (“CCE”) count under 21 U.S.C. § 848 based on the same conduct. Id. at 294–95. He was convicted of both crimes and received concurrent life sentences. The *6 question before the Court was whether the convictions and concurrent sentences violated the defendant’s Fifth Amend- ment right not to be punished twice for the same offense. The Court held that it did and ordered the lower court to vacate the lesser count. Id. at 307.

Under the familiar Blockburger test, if “the same act or transaction constitutes a violation of two distinct statutory provisions,” the double-jeopardy inquiry asks “whether each provision requires proof of a fact which the other does not.” Blockburger v. United States, 284 U.S. 299, 304 (1932). A lesser-included offense nests within the greater offense and therefore flunks the Blockburger test. Rutledge , 517 U.S. at 297 (“In subsequent applications of the [ Blockburger ] test, we have often concluded that two different statutes define the ‘same offense,’ typically because one is a lesser included offense of the other.”).

The Court began its analysis in Rutledge by noting that a conviction under the CCE statute requires proof that the defendant participated in a series of predicate drug crimes “in concert” with at least five other persons. Id. at 295; see also 21 U.S.C. § 848(c)(2)(A). The “in concert” element, the Court held, “requires proof of a conspiracy that would also violate § 846.” 517 U.S. at 300. This “straightforward applica- tion of the Blockburger test” led the Court to conclude that “conspiracy as defined in § 846 does not define a different offense from the CCE offense defined in § 848.” Id. The Court also noted that the CCE crime “is the more serious of the two, and … only one of its elements is necessary to prove a § 846 conspiracy.” Id. Accordingly, the Court held that a conspiracy to violate § 846 is a lesser-included offense of a factually coterminous § 848 enterprise crime and remanded *7 with instructions to vacate the lesser conviction and its concurrent sentence. Id. at 307.

Although Rutledge involved two drug crimes found in Title 21, the Court’s reasoning plainly applies in the analo- gous context of a child-exploitation enterprise. See, e.g. , United States v. Wayerski , 624 F.3d 1342, 1350–51 (11th Cir. 2010) (holding that under Rutledge , a child-pornography conspiracy is a lesser-included offense of a child-exploitation enterprise under § 2252A(g)). Title 18 defines a child- exploitation enterprise as “a series of” offenses involving child victims, comprising “three or more separate incidents,” and committed “in concert with three or more other per- sons.” § 2252A(g)(2). The two conspiracies charged in this case—a child-pornography conspiracy and a child- exploitation conspiracy—served as predicates for the enter- prise charge. The facts necessary to prove the two conspira- cies were wholly incorporated into the enterprise count; the jury’s verdict establishes as much. Applying Rutledge , then, the conspiracy offenses are lesser-included offenses of the enterprise count.

The government confesses the Rutledge error but argues that reversal is unwarranted because the error was not “obvious.” We disagree. The Rutledge rule is clear, long- standing, and directly applicable. Because the conspiracies are lesser-included offenses of the enterprise crime, multiple sentences violate the Double Jeopardy Clause. The convic- tions on count one and two should have been merged with the enterprise conviction prior to the imposition of sentence. The remedy is a remand for the district judge to exercise her discretion, in the first instance, to vacate either the convic- tions on the greater offense or the convictions on the lesser- *8 included offenses. Lanier v. United States , 220 F.3d 833, 841 (7th Cir. 2000) (“[W]hen the presumption against double punishment requires invalidation of the conviction for either the greater or lesser offense, the choice of which conviction to vacate rests with the sound discretion of the district court.”); United States v. Fischer , 205 F.3d 967, 970 n.2 (7th Cir. 2000) (“[W]hen a defendant is convicted of an offense and a lesser-included offense, the district court should decide which conviction to vacate.”).

B. Sufficiency of the Evidence

The defendants also argue that the government failed to prove all of the elements of the child-exploitation conspiracy charged in count two. As relevant here, the crime of child sexual exploitation includes the act of knowingly publishing “any notice or advertisement” to “receive, exchange, buy, produce, display, distribute, or reproduce” child pornogra- phy. § 2251(d)(1)(A). The defendants argue that a “notice” or “advertisement” implies a public component, but the evi- dence established only that they used a private, password- protected chat room to exchange child pornography with a limited group of individuals.

As a preliminary matter, we note that the jury’s special verdict is more than sufficient to support the § 2252A(g)(2) enterprise convictions even without the conspiracy predi- cates. The jury found that each defendant committed multi- ple predicate crimes against children. And the defendants do not challenge the sufficiency of the evidence supporting their convictions on the child-pornography conspiracy charged in count one. Still, on remand the judge may opt to vacate the greater rather than the lesser convictions as a *9 remedy for the Rutledge error, so we will proceed to decision on the challenge to count two.

On the merits, we can be brief. The phrase “any notice or advertisement” in § 2251(d) casts a wide net for this offense. The ordinary meaning of “notice” is a “warning or intima- tion of something.” Notice , W EBSTER ’ S T HIRD N EW I NTERNATIONAL D ICTIONARY (ed. 2002); see also Notice , N EW O XFORD A MERICAN D ICTIONARY (3d ed. 2010) (defining “notice” as a “notification or warning of something”). In everyday parlance, the term is not limited to warnings or notifications disseminated to the general public, and nothing about the context in which it is used here suggests a more limited meaning. Indeed, the Tenth Circuit has expressly rejected the interpretation the defendants have advanced, United States v. Franklin , 785 F.3d 1365, 1367–69 (10th Cir. 2015), and we see no reason to disagree. The thousands of file-sharing messages posted in this password-protected online chat room are easily sufficient to support the § 2251(d) convictions.

C. Unreasonable Sentences?

In their final argument, Gries and McCullars maintain that their sentences are unreasonably long. In particular, they attack the judge’s emphasis on the risk of recidivism. They also argue that their prison terms are excessive as compared to their coconspirators’ sentences.

District judges have broad discretion to prioritize and weigh the relevant sentencing factors under 18 U.S.C. § 3553(a). Appellate review for reasonableness is highly deferential; we will reverse only for an abuse of discretion. United States v. Carter , 538 F.3d 784, 789 (7th Cir. 2008). A *10 reviewing court’s “disagreement with how the judge weighted particular factors does not establish an abuse of discretion.” United States v. Reibel , 688 F.3d 868, 871 (7th Cir. 2012). And because the challenged sentences fall within properly calculated guidelines ranges, the defendants face an additional high hurdle: Guidelines sentences are “entitled to a presumption of reasonableness.” United States v. Grigsby , 692 F.3d 778, 792 (7th Cir. 2012).

Gries and McCullars have not overcome the presumption of reasonableness. When it comes to weighing the relevant sentencing factors, the boundaries of the district judge’s discretion are wide. Reibel , 688 F.3d at 872. Here the judge touched on the most salient sentencing factors: the im- portance of protecting children from sexual exploitation, the need to deter the defendants and others from participating in the market for child pornography, the broad scope and lengthy duration of the criminal enterprise, the large number of people involved, the vast amount of pornography they exchanged, and the sheer depravity of the crime. Given the nature and scope of this criminal enterprise, the judge reasonably concluded that the risk of recidivism is high.

The argument that Gries and McCullars were treated more harshly than their coconspirators does nothing to rebut the presumption of reasonableness. See Grigsby , 692 F.3d at 793. Simply put, these defendants were not similarly situated to the others; the other chat-room participants cooperated with investigators, pleaded guilty, and some testified for the government. See United States v. Statham , 581 F.3d 548, 556 (7th Cir. 2009). There is nothing unreasonable about impos- ing different sentences on differently situated members of a conspiracy.

R EVERSED AND R EMANDED WITH I NSTRUCTIONS .

[1] “No person shall … be subject for the same offence to be twice put in jeopardy of life or limb … .” U.S. C ONST . amend. V.