## Algorithm

B. Modulo Sum
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 ≤ 1062 ≤ 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
Copy
`3 51 2 3`
output
Copy
`YES`
input
Copy
`1 65`
output
Copy
`NO`
input
Copy
`4 63 1 1 3`
output
Copy
`YES`
input
Copy
`6 65 5 5 5 5 5`
output
Copy
`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.

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <stdio.h>
#include <memory.h>

using namespace std;

int const N = 1e6 + 1;
int n, m, a[N], dp[1001][1001][2];

bool rec(int i, int sum, bool take) {
if(sum == 0 && take)
return true;

if(i == n)
return false;

int &ret = dp[i][sum][take];
if(ret != -1) return ret;
ret = false;

return ret = (rec(i + 1, (sum + a[i]) % m, true) || rec(i + 1, sum % m, take));
}

int main() {
scanf("%d %d", &n, &m);
for(int i = 0; i < n; ++i)
scanf("%d", a + i);

if(n > m) {
puts("YES");
return 0;
}

memset(dp, -1, sizeof dp);
if(rec(0, 0, 0))
puts("YES");
else
puts("NO");

return 0;
}``````
Copy The Code &

Input

cmd
3 5
1 2 3

Output

cmd
YES