数字运算，判断一个数是否接近素数



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



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-numerical operations, judge whether a few close-A few number n is a number such that the sum of its digits divides itself. For example, 111 n is a 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 number n if the sum of its digits divides its value. Given b (2 lt; = b lt; = 10) and a number in base b, determine whether it n is a number or not. Input 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 n is a number, and "no" otherwise. Sample Input 101112 110 101236 1000 8