# Big set

Author: mathforces
Problem has been solved: 15 times

Русский язык | English Language

All positive integer numbers less than 2022 are written on the board. Lin and Nil wrote down (possibly same) of them in their notebooks, and Lin wrote exactly 1011 numbers. It turned out that the largest number written by Lin equals the smallest number written by Nil. Let $x$ be the number of ways in which this could happen. Find the remainder when dividing $x$ by $10 ^ 7$.