Codeforces 792B. Counting-out Rhyme

B. Counting-out Rhyme

time limit per test：

1 second

memory limit per test：

256 megabytes

input：

standard input

output：

standard output

n children are standing in a circle and playing the counting-out game. Children are numbered clockwise from 1 to n. In the beginning, the first child is considered the leader. The game is played in k steps. In the i-th step the leader counts out ai people in clockwise order, starting from the next person. The last one to be pointed at by the leader is eliminated, and the next player after him becomes the new leader.

For example, if there are children with numbers [8, 10, 13, 14, 16] currently in the circle, the leader is child 13 and ai = 12, then counting-out rhyme ends on child 16, who is eliminated. Child 8 becomes the leader.

You have to write a program which prints the number of the child to be eliminated on every step.

Input

The first line contains two integer numbers n and k (2 ≤ n ≤ 100, 1 ≤ k ≤ n - 1).

The next line contains k integer numbers a1, a2, ..., ak (1 ≤ ai ≤ 109).

Output

Print k numbers, the i-th one corresponds to the number of child to be eliminated at the i-th step.

Examples

input

7 5
10 4 11 4 1

output

4 2 5 6 1 

input

3 2
2 5

output

3 2 

Note

Let's consider first example:

• In the first step child 4 is eliminated, child 5 becomes the leader.
• In the second step child 2 is eliminated, child 3 becomes the leader.
• In the third step child 5 is eliminated, child 6 becomes the leader.
• In the fourth step child 6 is eliminated, child 7 becomes the leader.
• In the final step child 1 is eliminated, child 3 becomes the leader.

题目链接：http://codeforces.com/problemset/problem/792/B

提意：编号1~n的n个人人围成一个圈。k此操作，每次操作为将执行者后面的第a个人剔除出去，下一次的执行者为剔除出去的后一个人，第一次操作的执行者编号为1。

思路：模拟。将a对cou取模，cou为每次操作后的剩余人数。

代码：

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
int sign[];
int main()
{
    int n,k;
    int a;
    scanf("%d%d",&n,&k);
    int cou=n,start=;
    memset(sign,,sizeof(sign));
    for(int i=; i<=k; i++)
    {
        scanf("%d",&a);
        a=a%cou;
        int t=;
        while(t<=a)
        {
            start++;
            if(start>n) start-=n;
            if(sign[start]) continue;
            if(t==a) {sign[start]=;cout<<start<<" ";}
            t++;
        }
        cou--;
    }
    return ;
}