Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Martian Luck

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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*(3504_{7}) = *d*((3 + 5 + 0 + 4)_{7}) = *d*(15_{7}) = *d*((1 + 5)_{7}) = *d*(6_{7}) = 6_{7}. 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}.

Input

The first line contains three integers *k*, *b* and *n* (2 ≤ *k* ≤ 10^{9}, 0 ≤ *b* < *k*, 1 ≤ *n* ≤ 10^{5}).

The second line contains string *s* as a sequence of *n* integers, representing digits in the *k*-base notation: the *i*-th integer equals *a*_{i} (0 ≤ *a*_{i} < *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 С++. 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".

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/27/2017 16:13:15 (c3).

Desktop version, switch to mobile version.
User lists

Name |
---|