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.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Enumeration;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Map;
import java.util.Properties;

/**
 * Works good for CF
 * 
 * @author cykeltillsalu
 */
public class EAgain {

	// some local config
	static boolean test = false;
	static String testDataFile = "testdata.txt";
	static String feedFile = "feed.txt";
	CompetitionType type = CompetitionType.CF;
	private static String ENDL = "\n";

	// solution
	private void solve() throws Throwable {

		int k = iread(), b = iread(), n = iread();
		long ans = 0;
		if(b == 0){
			long cnt = 0;
			for (int i = 0; i < n; i++) {
				int val = iread();
				if(val == 0){
					cnt ++;
				} else {
					ans += cnt*(cnt+1)/2;
					cnt = 0;
				}
			}
			ans += cnt*(cnt+1)/2;
		} else {
			Map<Integer, Integer> map = new HashMap<Integer, Integer>();
			map.put(0, 1);
			int next = 0;
			int zcnt = 0;
			for (int i = 0; i < n; i++) {
				int val = iread();
				next = (next + val) %(k-1);
				int friend = (next - b + k -1)%(k-1);
				ans += map.containsKey(friend) ? map.get(friend) : 0;
				if(val == 0){
					zcnt ++;
				} else {
					zcnt = 0;
				}
				Integer integer = map.get(next);
				if(integer == null){
					integer = 0;
				}
				map.put(next, integer + 1);
				if(b == k -1 ){
					ans -= zcnt;
				}
			}
		}
		
		System.out.println(ans);
	}

	public int iread() throws Exception {
		return Integer.parseInt(wread());
	}

	public double dread() throws Exception {
		return Double.parseDouble(wread());
	}

	public long lread() throws Exception {
		return Long.parseLong(wread());
	}

	public String wread() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) throws Throwable {

		if (test) { // run all cases from testfile:
			BufferedReader testdataReader = new BufferedReader(new FileReader(testDataFile));
			String readLine = testdataReader.readLine();
			int casenr = 0;
			out: while (true) {
				BufferedWriter w = new BufferedWriter(new FileWriter(feedFile));
				if (!readLine.equalsIgnoreCase("input")) {
					break;
				}
				while (true) {
					readLine = testdataReader.readLine();
					if (readLine.equalsIgnoreCase("output")) {
						break;
					}
					w.write(readLine + "\n");
				}
				w.close();
				System.out.println("Answer on case " + (++casenr) + ": ");

				new EAgain().solve();
				System.out.println("Expected answer: ");

				while (true) {
					readLine = testdataReader.readLine();

					if (readLine == null) {
						break out;
					}
					if (readLine.equalsIgnoreCase("input")) {
						break;
					}
					System.out.println(readLine);
				}
				System.out.println("----------------");
			}
			testdataReader.close();
		} else { // run on server
			new EAgain().solve();
		}
		out.close();
	}

	public EAgain() throws Throwable {
		if (test) {
			in = new BufferedReader(new FileReader(new File(feedFile)));
		}
	}

	InputStreamReader inp = new InputStreamReader(System.in);
	BufferedReader in = new BufferedReader(inp);
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

	enum CompetitionType {
		CF, OTHER
	};
}