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1156.   Niven Numbers
Time Limit: 1.0 Seconds   Memory Limit: 65536K
Total Runs: 3753   Accepted Runs: 1270    Multiple test files

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.

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

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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