← 返回题目

题库练习 Factorial Divisibility

← 上一题下一题 →

A15535 | $Factorial Divisibility$

时间限制1s

内存限制256MB

通过 / 提交0/0

题目描述

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 $5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 = 120$ .

输入格式

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.

输出格式

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.

输入输出样例

输入 #1

6 4
3 2 2 2 3 3

输出 #1

Yes

输入 #2

8 3
3 2 2 2 2 2 1 1

输出 #2

Yes

输入 #3

7 8
7 7 7 7 7 7 7

输出 #3

No

输入 #4

10 5
4 3 2 1 4 3 2 4 3 4

输出 #4

No

输入 #5

2 500000
499999 499999

输出 #5

No

C++ 编辑器

输入

输出