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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.
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.
For each case, print "yes" on a line if the given number is a Niven number, and "no" otherwise.
10 111 2 110 10 123 6 1000 8 2314 0
yes yes no yes no