Martian Luck

You know that the Martians use a number system with base k. Digit b (0 ≤ b < k) is considered lucky, as the first contact between the Martians and the Earthlings occurred in year b (by Martian chronology).

A digital root d(x) of number x is a number that consists of a single digit, resulting after cascading summing of all digits of number x. Word "cascading" means that if the first summing gives us a number that consists of several digits, then we sum up all digits again, and again, until we get a one digit number.

For example, d(3504₇) = d((3 + 5 + 0 + 4)₇) = d(15₇) = d((1 + 5)₇) = d(6₇) = 6₇. In this sample the calculations are performed in the 7-base notation.

If a number's digital root equals b, the Martians also call this number lucky.

You have string s, which consists of n digits in the k-base notation system. Your task is to find, how many distinct substrings of the given string are lucky numbers. Leading zeroes are permitted in the numbers.

Note that substring s[i... j] of the string s = a₁a₂... a_n (1 ≤ i ≤ j ≤ n) is the string a_ia_i + 1... a_j. Two substrings s[i₁... j₁] and s[i₂... j₂] of the string s are different if either i₁ ≠ i₂ or j₁ ≠ j₂.