Divisibility Check

Problem Background

Special for beginners, ^_^

Problem Description

For a given sequence of positive integers, insert a + or - sign before each number and compute their sum. For example, the sequence 1, 2, 4 has 8 possible signed sums:

(+1) + (+2) + (+4) = 7
(+1) + (+2) + (-4) = -1
(+1) + (-2) + (+4) = 3
(+1) + (-2) + (-4) = -5
(-1) + (+2) + (+4) = 5
(-1) + (+2) + (-4) = -3
(-1) + (-2) + (+4) = 1
(-1) + (-2) + (-4) = -7

If at least one of all the results is divisible by the integer $k$, we say this sequence of positive integers is divisible by $k$. For example, the sequence above is divisible by $3, 5, 7$ but not by $2, 4, 6, 8, \dots$. Note that $0, -3, -6, -9, \dots$ are all considered multiples of $3$.

Input Format

The first line contains two numbers: $N$ ($2 < N < 10000$) and $k$ ($2 < k < 100$), where $N$ is the number of integers in the sequence and $k$ is the divisor. The second line gives the $N$ integers of the sequence, each between $0$ and $10000$ (possibly with repeats).

Output Format

If the sequence is divisible by $k$, output YES; otherwise output NO. (Note: all uppercase letters.)

Sample Input 1

3 2
1 2 4

Sample Output 1

NO

Constraints

1s, 1024KiB for each test case.