While Mike was walking in the subway, all the stuff in his back-bag dropped on the ground. There were several fax messages among them. He concatenated these strings in some order and now he has string *s*.

He is not sure if this is his own back-bag or someone else's. He remembered that there were exactly *k* messages in his own bag, each was a palindrome string and all those strings had the same length.

He asked you to help him and tell him if he has worn his own back-bag. Check if the given string *s* is a concatenation of *k* palindromes of the same length.
The first line of input contains string *s* containing lowercase English letters (1 ≤ |*s*| ≤ 1000).

The second line contains integer *k* (1 ≤ *k* ≤ 1000).
# LUOGU_RID: 100308836
#include <stdio.h>

int main()
{
    int t;
    scanf("%d", &t);
    while (t--)
    {
        int n, k;
        scanf("%d %d", &n, &k);
        char s[n+1];
        scanf("%s", s);
        int i = 0;
        int isUp = 1;
        while (k > 0)
        {
            if (s[i] == '0')
            {
                k -= (1 << (n - i - 1));
                isUp = !isUp;
            }
            else
            {
                k -= (1 << i);
            }
            i++;
        }
        printf("%s\n", isUp ? "Up" : "Down");
    }
    return 0;
}