What is the burden of proving constructive amendment to a criminal charge?

"We review de novo challenges to the sufficiency of the evidence underlying a criminal conviction, but a defendant bears a heavy burden . . . because we review evidence on a sufficiency challenge in the light most favorable to the government and draw all inferences in favor of the government." United States v. Lee, 723 F.3d 134, 143 (2d Cir. 2013) (internal quotation marks, citations, and brackets omitted) (emphasis in original). "We will uphold a judgment of conviction if any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Id. (internal quotation marks and brackets omitted) (emphasis in original).

"A constructive amendment of an indictment occurs when either the proof at trial or the trial court's jury instructions so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject of the grand jury's indictment." United States v. Dupre, 462 F.3d 131, 140 (2d Cir. 2006) (internal quotation marks omitted). "By contrast, a variance occurs when the charging terms of the indictment are left unaltered, but the evidence at trial proves facts materially different from those alleged in the indictment," and requires the defendant to demonstrate prejudice by showing that the defendant was not informed of the charges against him. Id. (internal quotation marks and brackets omitted).