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... an (1≤i≤j≤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≠i2 or j1≠j2.
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.
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.
10 5 6
3 2 0 5 6 1
5
7 6 4
3 5 0 4
1
257 0 3
0 0 256
3
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".