Problem:
Score : 500 points

Problem Statement

Takahashi has a string S of length N consisting of digits from 0 through 9.

He loves the prime number P. He wants to know how many non-empty (contiguous) substrings of S - there are N \times (N + 1) / 2 of them - are divisible by P when regarded as integers written in base ten.

Here substrings starting with a 0 also count, and substrings originated from different positions in S are distinguished, even if they are equal as strings or integers.

Compute this count to help Takahashi.

Constraints

1 \leq N \leq 2 \times 10^5

S consists of digits.

|S| = N

2 \leq P \leq 10000

P is a prime number.

Input

Input is given from Standard Input in the following format:

N P
S

Output

Print the number of non-empty (contiguous) substrings of S that are divisible by P when regarded as an integer written in base ten.

Sample Input 1

4 3
3543

Sample Output 1

6

Here S = 3543. There are ten non-empty (contiguous) substrings of S:

3: divisible by 3.

35: not divisible by 3.

354: divisible by 3.

3543: divisible by 3.

5: not divisible by 3.

54: divisible by 3.

543: divisible by 3.

4: not divisible by 3.

43: not divisible by 3.

3: divisible by 3.

Six of these are divisible by 3, so print 6.

Sample Input 2

4 2
2020

Sample Output 2

10

Here S = 2020. There are ten non-empty (contiguous) substrings of S, all of which are divisible by 2, so print 10.

Note that substrings beginning with a 0 also count.

Sample Input 3

20 11
33883322005544116655

Sample Output 3

68

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Diagnostics;
using Debug = System.Diagnostics.Trace;
using SB = System.Text.StringBuilder;
using static System.Math;
using Number = System.Int32;
using System.Numerics;
namespace Program {
	public class Solver {
		Random rnd = new Random(0);
		public void Solve() {
			var n = ri;
			var P = ri;
			var dp = new int[P];
			var s = rs;
			//[l,r)
			var ans = 0L;
			var rev = (int)BigInteger.ModPow(10 % P, P - 2, P);
			Action<int, int, int[]> dfs = null;
			dfs = (l, r, cnt) => {
				if (r - l == 1) {
					if ((s[l] - '0') % P == 0) ans++;
					return;
				}

				var m = (l + r) / 2;

				dfs(l, m, cnt);
				dfs(m, r, cnt);
				for (int i = m - 1, v = 0, p = 1; i >= l; i--, p = (p * 10) % P) {
					v = (v + (s[i] - '0') * p) % P;
					cnt[v]++;
				}
				for (int i = m, v = 0, p = rev; i < r; i++, p = (p * rev) % P) {
					v = (v * 10 + s[i] - '0') % P;
					var rv = (P - v) * p % P;
					ans += cnt[rv];
				}
				for (int i = m - 1, v = 0, p = 1; i >= l; i--, p = (p * 10) % P) {
					v = (v + (s[i] - '0') * p) % P;
					cnt[v]--;
				}
			};
			dfs(0, n, new int[P]);
			Console.WriteLine(ans);
		}
		const long INF = 1L << 60;
		static int[] dx = { -1, 0, 1, 0 };
		static int[] dy = { 0, 1, 0, -1 };
		int ri { get { return sc.Integer(); } }
		long rl { get { return sc.Long(); } }
		double rd { get { return sc.Double(); } }
		string rs { get { return sc.Scan(); } }
		public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

		static T[] Enumerate<T>(int n, Func<int, T> f) {
			var a = new T[n];
			for (int i = 0; i < a.Length; ++i) a[i] = f(i);
			return a;
		}
		static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
	}
}

#region main
static class Ex {
	static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
	static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
		return string.Join(st, ie);
	}
	static public void Main() {
		Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = true });
		var solver = new Program.Solver();
		//* 
		var t = new System.Threading.Thread(solver.Solve, 50000000);
		//t.Start();
		//t.Join();
		//*/
		solver.Solve();
		Console.Out.Flush();
	}
}
#endregion
#region Ex
namespace Program.IO {
	using System.IO;
	using System.Text;
	using System.Globalization;

	public class Printer : StreamWriter {
		public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
		public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	}

	public class StreamScanner {
		public StreamScanner(Stream stream) { str = stream; }

		public readonly Stream str;
		private readonly byte[] buf = new byte[1024];
		private int len, ptr;
		public bool isEof = false;
		public bool IsEndOfStream { get { return isEof; } }

		private byte read() {
			if (isEof) return 0;
			if (ptr >= len) {
				ptr = 0;
				if ((len = str.Read(buf, 0, 1024)) <= 0) {
					isEof = true;
					return 0;
				}
			}
			return buf[ptr++];
		}

		public char Char() {
			byte b = 0;
			do b = read(); while ((b < 33 || 126 < b) && !isEof);
			return (char)b;
		}
		public string Scan() {
			var sb = new StringBuilder();
			for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
			return sb.ToString();
		}
		public string ScanLine() {
			var sb = new StringBuilder();
			for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
			return sb.ToString();
		}
		public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
		public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
		public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
	}
}

#endregion

#region ModInt
/// <summary>
/// [0,<see cref="Mod"/>) までの値を取るような数
/// </summary>
public struct ModInt {
	/// <summary>
	/// 剰余を取る値．
	/// </summary>
	public const long Mod = 998244353;

	/// <summary>
	/// 実際の数値．
	/// </summary>
	public long num;
	/// <summary>
	/// 値が <paramref name="n"/> であるようなインスタンスを構築します．
	/// </summary>
	/// <param name="n">インスタンスが持つ値</param>
	/// <remarks>パフォーマンスの問題上，コンストラクタ内では剰余を取りません．そのため，<paramref name="n"/> ∈ [0,<see cref="Mod"/>) を満たすような <paramref name="n"/> を渡してください．このコンストラクタは O(1) で実行されます．</remarks>
	public ModInt(long n) { num = n; }
	/// <summary>
	/// このインスタンスの数値を文字列に変換します．
	/// </summary>
	/// <returns>[0,<see cref="Mod"/>) の範囲内の整数を 10 進表記したもの．</returns>
	public override string ToString() { return num.ToString(); }
	public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
	public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
	public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
	public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }

	/// <summary>
	/// 与えられた 2 つの数値からべき剰余を計算します．
	/// </summary>
	/// <param name="v">べき乗の底</param>
	/// <param name="k">べき指数</param>
	/// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
	public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }

	/// <summary>
	/// 与えられた 2 つの数値からべき剰余を計算します．
	/// </summary>
	/// <param name="v">べき乗の底</param>
	/// <param name="k">べき指数</param>
	/// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
	public static ModInt Pow(long v, long k) {
		long ret = 1;
		for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
			if ((k & 1) == 1) ret = ret * v % Mod;
		return new ModInt(ret);
	}
	/// <summary>
	/// 与えられた数の逆元を計算します．
	/// </summary>
	/// <param name="v">逆元を取る対象となる数</param>
	/// <returns>逆元となるような値</returns>
	/// <remarks>法が素数であることを仮定して，フェルマーの小定理に従って逆元を O(log N) で計算します．</remarks>
	public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
}
#endregion
#region SegTree Operator
public interface IData<T> {
	T Merge(T l, T r);
	T Identity { get; }
	T InitValue { get; }
}
#endregion
#region Segment Tree

public class SegmentTree<T, U>
   where U : struct, IData<T> {
	int sz;
	int n;
	T[] data;
	U op;
	public SegmentTree(int size) {
		sz = size;
		n = 1;
		while (n < size) n *= 2;
		data = new T[n * 2];
		for (int i = 0; i < data.Length; i++)
			data[i] = op.InitValue;
	}
	public SegmentTree(T[] a) {
		sz = a.Length;
		n = 1;
		while (n < sz) n *= 2;
		data = new T[n * 2];
		for (int i = 0; i < n; i++)
			data[i + n] = (i < a.Length) ? a[i] : op.InitValue;
		for (int i = n - 1; i >= 0; i--)
			data[i] = op.Merge(data[i * 2], data[i * 2 + 1]);
	}
	public void Update(int k, T v) {
		k += n;
		data[k] = v;
		for (k = k / 2; k > 0; k /= 2)
			data[k] = op.Merge(data[k * 2], data[k * 2 + 1]);

	}
	public T Query(int a, int b) { return query(a, b, 1, 0, n); }
	private T query(int a, int b, int k, int l, int r) {
		if (r <= a || b <= l)
			return op.Identity;
		if (a <= l && r <= b)
			return data[k];
		else {
			var vl = query(a, b, k * 2, l, (l + r) / 2);
			var vr = query(a, b, k * 2 + 1, (l + r) / 2, r);
			return op.Merge(vl, vr);
		}
	}
	public T[] Items {
		get {
			var ret = new T[sz];
			for (int i = 0; i < sz; i++)
				ret[i] = data[i + n];
			return ret;
		}
	}

}
#endregion
#region RmQ
public class RmQ : SegmentTree<long, MinData> {
	public RmQ(int size) : base(size) { }
}
public struct MinData : IData<long> {
	public long InitValue { get { return 0; } }
	public long Identity { get { return long.MaxValue; } }
	public long Merge(long l, long r) { return Math.Min(l, r); }


}
#endregion
#region RMQ
public class RMQ : SegmentTree<long, MaxData> {
	public RMQ(int size) : base(size) { }
}
public struct MaxData : IData<long> {
	public long Identity { get { return long.MinValue; } }

	public long InitValue { get { return 0; } }

	public long Merge(long l, long r) { return Math.Max(l, r); }
}
#endregion