B. Factorial Divisibilitytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an integer x and an array of integers a_1, a_2, \ldots, a_n. You have to determine if the number a_1! + a_2! + \ldots + a_n! is divisible by x!.Here k! is a factorial of k — the product of all positive integers less than or equal to k. For example, 3! = 1 \cdot 2 \cdot 3 = 6, and 5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120.InputThe first line contains two integers n and x (1 \le n \le 500\,000, 1 \le x \le 500\,000).The second line contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le x) — elements of given array.OutputIn the only line print "Yes" (without quotes) if a_1! + a_2! + \ldots + a_n! is divisible by x!, and "No" (without quotes) otherwise.ExamplesInput
6 4
3 2 2 2 3 3
Output
Yes
Input
8 3
3 2 2 2 2 2 1 1
Output
Yes
Input
7 8
7 7 7 7 7 7 7
Output
No
Input
10 5
4 3 2 1 4 3 2 4 3 4
Output
No
Input
2 500000
499999 499999
Output
No
NoteIn the first example 3! + 2! + 2! + 2! + 3! + 3! = 6 + 2 + 2 + 2 + 6 + 6 = 24. Number 24 is divisible by 4! = 24.In the second example 3! + 2! + 2! + 2! + 2! + 2! + 1! + 1! = 18, is divisible by 3! = 6.In the third example 7! + 7! + 7! + 7! + 7! + 7! + 7! = 7 \cdot 7!. It is easy to prove that this number is not divisible by 8!.
6 4
3 2 2 2 3 3

Yes 
['math', 'number theory', '*1600']