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 = a 1 a 2... a n (1 ≤ i ≤ j ≤ n ) is the string a i a i + 1... a j . Two substrings s[i 1... j 1] and s[i 2... j 2] of the string s are different if either i 1 ≠ i 2 or j 1 ≠ j 2 .

输入描述:

The first line contains three integers k, b and n (2 ≤ k ≤ 109, 0 ≤ b k, 1 ≤ n ≤ 105).The second line contains string s as a sequence of n integers, representing digits in the k-base notation: the i-th integer equals ai (0 ≤ ai k) — the i-th digit of string s. The numbers in the lines are space-separated.

输出描述:

Print a single integer — the number of substrings that are lucky numbers.Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

备注:

In the first sample the following substrings have the sought digital root: s[1... 2] = "3 2", s[1... 3] = "3 2 0", s[3... 4] = "0 5", s[4... 4] = "5" and s[2... 6] = "2 0 5 6 1".