## GUPTA MECHANICAL

IN THIS WEBSITE I CAN TELL ALL ABOUT TECH. TIPS AND TRICKS APP REVIEWS AND UNBOXINGS ALSO TECH. NEWS .............

# [Solution] Factorial Divisibility Codeforces Solution

D. Factorial Divisibility
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an integer $x$ and an array of integers ${a}_{1},{a}_{2},\dots ,{a}_{n}$. You have to determine if the number ${a}_{1}!+{a}_{2}!+\dots +{a}_{n}!$ 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 $5!=1\cdot 2\cdot 3\cdot 4\cdot 5=120$.

Input

The first line contains two integers $n$ and $x$ ($1\le n\le 500\phantom{\rule{thinmathspace}{0ex}}000$$1\le x\le 500\phantom{\rule{thinmathspace}{0ex}}000$).

The second line contains $n$ integers ${a}_{1},{a}_{2},\dots ,{a}_{n}$ ($1\le {a}_{i}\le x$) — elements of given array.

Output

In the only line print "Yes" (without quotes) if ${a}_{1}!+{a}_{2}!+\dots +{a}_{n}!$ is divisible by $x!$, and "No" (without quotes) otherwise.

Note

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 $8!$.