You are given a sequence of numbers a1, a2, ..., an, and a number m.

Check if it is possible to choose a non-empty subsequence aij such that the sum of numbers in this subsequence is divisible by m.

Input

The first line contains two numbers, n and m (1 ≤ n ≤ 106, 2 ≤ m ≤ 103) — the size of the original sequence and the number such that sum should be divisible by it.

The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109).

Output

In the single line print either "YES" (without the quotes) if there exists the sought subsequence, or "NO" (without the quotes), if such subsequence doesn't exist.

Examples

Input

3 5
1 2 3


Output

YES


Input

1 6
5


Output

NO


Input

4 6
3 1 1 3


Output

YES


Input

6 6
5 5 5 5 5 5


Output

YES

Note

In the first sample test you can choose numbers 2 and 3, the sum of which is divisible by 5.

In the second sample test the single non-empty subsequence of numbers is a single number 5. Number 5 is not divisible by 6, that is, the sought subsequence doesn't exist.

In the third sample test you need to choose two numbers 3 on the ends.

In the fourth sample test you can take the whole subsequence.
#577B

a = list(map(int, input().split(" ")))
n = a[0]
m = a[1]
arr = list(map(int, input().split(" ")))
d = dict()

if n > (m / 2) * (m - 1):
	print("YES")
else:
	for j in range(m):
		d[(1, j)] = 0

	r = arr[0] % m
	d[(1, r)] = 1

	for i in range(2, n + 1):
		r = arr[i-1] % m
		for j in range(m):
			d[(i, j)] = 0
		d[(i, r)] = 1
		for j in range(m):
			if d[(i - 1, j)] == 1:
				d[(i, j)] = 1
				d[(i, (j + r) % m)] = 1

	if d[n, 0] == 1:
		print("YES")
	else:
		print("NO")


