You know that the Martians use a number system with base k. Digit b (0 \le b \lt 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... an (1 \le i \le j \le n) is the string aiai+1... aj. Two substrings s[i1... j1] and s[i2... j2] of the string s are different if either i1 \neq i2 or j1 \neq j2.

The first line contains three integers k, b and n (2 \le k \le 109, 0 \le b \lt k, 1 \le n \le 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 \le ai \lt k) - the i-th digit of string s. The numbers in the lines are space-separated.

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 C++. It is preferred to use the cin, cout streams or the %I64d specifier.

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".