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.

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 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".
import java.io.*;
import java.util.*;

public class E implements Runnable {
	private MyIntegerScanner in;
	private PrintWriter out;

	int mod(int n, int mod) {
		int ans = n % mod;
		if (ans < 0) {
			ans += mod;
		}
		return ans;
	}

	private void solve() {
		int k = in.nextInt(), b = in.nextInt(), n = in.nextInt();
		int[] num = new int[n];
		for (int i = 0; i < n; ++i) {
			num[i] = in.nextInt();
		}

		Map<Integer, Integer> mods = new HashMap<Integer, Integer>();
		int add = 0;
		long ans = 0;

		if (b == 0) {
			int zero = 0;
			for (int i = 0; i < n; ++i) {
				if (num[i] == 0) {
					++zero;
					ans += zero;
				} else {
					zero = 0;
				}
			}
			out.println(ans);
			return;
		}

		int nb = b % (k - 1);
		for (int i = 0; i < n; ++i) {
			int cn = num[i] % (k - 1);
			add = mod(add + cn, k - 1);
			int key = mod(cn - add, k - 1);
			Integer was = mods.get(key);
			if (was == null) {
				was = 0;
			}
			mods.put(key, was + 1);
			Integer delta = mods.get(mod(nb - add, k - 1));
			if (delta != null) {
				ans += delta;
			}
		}

		if (b == k - 1) {
			int zero = 0;
			for (int i = 0; i < n; ++i) {
				if (num[i] == 0) {
					++zero;
					ans -= zero;
				} else {
					zero = 0;
				}
			}
		}
		out.println(ans);
	}

	@Override
	public void run() {
		in = new MyIntegerScanner();
		out = new PrintWriter(System.out);
		solve();
		in.close();
		out.close();
	}

	public static void main(String[] args) {
		new E().run();
	}

	class MyIntegerScanner {
		private BufferedReader br;

		public MyIntegerScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public MyIntegerScanner(String fileName) {
			try {
				br = new BufferedReader(new FileReader(fileName));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			try {
				br.close();
			} catch (IOException e) {
				e.printStackTrace();
			}
		}

		public int nextInt() {
			try {
				int c = br.read();
				while (c != '-' && (c < '0' || c > '9')) {
					c = br.read();
				}
				boolean sign = c == '-';
				if (sign) {
					c = br.read();
				}
				int ans = 0;
				while (c >= '0' && c <= '9') {
					ans = ans * 10 + c - '0';
					c = br.read();
				}
				return sign ? -ans : ans;
			} catch (IOException e) {
				e.printStackTrace();
				return -1;
			}
		}

		public long nextLong() {
			try {
				int c = br.read();
				while (c != '-' && (c < '0' || c > '9')) {
					c = br.read();
				}
				boolean sign = c == '-';
				if (sign) {
					c = br.read();
				}
				long ans = 0;
				while (c >= '0' && c <= '9') {
					ans = ans * 10 + c - '0';
					c = br.read();
				}
				return sign ? -ans : ans;
			} catch (IOException e) {
				e.printStackTrace();
				return -1;
			}
		}
	}
}