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ZOJ Problem Set - 1154
Niven Numbers

Time Limit: 2 Seconds      Memory Limit: 65536 KB

A Niven number is a number such that the sum of its digits divides itself. For example, 111 is a Niven number because the sum of its digits is 3, which divides 111. We can also specify a number in another base b, and a number in base b is a Niven number if the sum of its digits divides its value.

Given b (2 <= b <= 10) and a number in base b, determine whether it is a Niven number or not.


This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.


Input

You will be given a number of test cases. Each line of input contains the base b, followed by a string of digits representing a positive integer in that base. There are no leading zeroes. The input is terminated by a line consisting of 0 alone.


Output

For each case, print "yes" on a line if the given number is a Niven number, and "no" otherwise.


Sample Input

1

10 111
2 110
10 123
6 1000
8 2314
0


Sample Output

yes
yes
no
yes
no


Source: East Central North America 1999, Practice
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