# Niven Numbers

Time Limit: 1 Second Memory Limit: 32768 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 noSubmit

Source: East Central North America 1999, Practice