A10019. Modulo Sum
编程题
普及/提高-
知识点
题目描述
You are given a sequence of numbers $a_{1},a_{2},...,a_{n}$ , and a number $m$ .
Check if it is possible to choose a non-empty subsequence $a_{ij}$ such that the sum of numbers in this subsequence is divisible by $m$ .
Check if it is possible to choose a non-empty subsequence $a_{ij}$ such that the sum of numbers in this subsequence is divisible by $m$ .
输入格式
The first line contains two numbers, $n$ and $m$ ( $1<=n<=10^{6}$ , $2<=m<=10^{3}$ ) — the size of the original sequence and the number such that sum should be divisible by it.
The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=10^{9}$ ).
The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=10^{9}$ ).
输出格式
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.
输入输出样例
输入 #1
3 5 1 2 3
输出 #1
YES
输入 #2
1 6 5
输出 #2
NO
输入 #3
4 6 3 1 1 3
输出 #3
YES
输入 #4
6 6 5 5 5 5 5 5
输出 #4
YES
说明/提示
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.
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.