Problem3513--Martian Luck

3513: Martian Luck

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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≤ijn) is the string aiai+1... aj. Two substrings s[i1... j1] and s[i2... j2] of the string s are different if either i1i2 or j1j2.

Input

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.

Output

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.

Examples
Input
10 5 6
3 2 0 5 6 1
Output
5
Input
7 6 4
3 5 0 4
Output
1
Input
257 0 3
0 0 256
Output
3
Note

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".

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