CF1753B Factorial Divisibility

You 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 $ .

The 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.

In the only line print "Yes" (without quotes) if $ a_1! + a_2! + \ldots + a_n! $ is divisible by $ x! $ , and "No" (without quotes) otherwise.

In 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! $ .