Problem:
Score : 500 points

Problem Statement

You are given two integer sequences S and T of length N and M, respectively, both consisting of integers between 1 and 10^5 (inclusive).

In how many pairs of a subsequence of S and a subsequence of T do the two subsequences are the same in content?

Here the subsequence of A is a sequence obtained by removing zero or more elements from A and concatenating the remaining elements without changing the order.

For both S and T, we distinguish two subsequences if the sets of the indices of the removed elements are different, even if the subsequences are the same in content.

Since the answer can be tremendous, print the number modulo 10^9+7.

Constraints

1 \leq N, M \leq 2 \times 10^3

The length of S is N.

The length of T is M.

1 \leq S_i, T_i \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
S_1 S_2 ... S_{N-1} S_{N}
T_1 T_2 ... T_{M-1} T_{M}

Output

Print the number of pairs of a subsequence of S and a subsequence of T such that the subsequences are the same in content, modulo 10^9+7.

Sample Input 1

2 2
1 3
3 1

Sample Output 1

3

S has four subsequences: (), (1), (3), (1, 3).

T has four subsequences: (), (3), (1), (3, 1).

There are 1 \times 1 pair of subsequences in which the subsequences are both (), 1 \times 1 pair of subsequences in which the subsequences are both (1), and 1 \times 1 pair of subsequences in which the subsequences are both (3), for a total of three pairs.

Sample Input 2

2 2
1 1
1 1

Sample Output 2

6

S has four subsequences: (), (1), (1), (1, 1).

T has four subsequences: (), (1), (1), (1, 1).

There are 1 \times 1 pair of subsequences in which the subsequences are both (), 2 \times 2 pairs of subsequences in which the subsequences are both (1), and 1 \times 1 pair of subsequences in which the subsequences are both (1,1), for a total of six pairs.
Note again that we distinguish two subsequences if the sets of the indices of the removed elements are different, even if the subsequences are the same in content.

Sample Input 3

4 4
3 4 5 6
3 4 5 6

Sample Output 3

16

Sample Input 4

10 9
9 6 5 7 5 9 8 5 6 7
8 6 8 5 5 7 9 9 7

Sample Output 4

191

Sample Input 5

20 20
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Output 5

846527861

Be sure to print the number modulo 10^9+7.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

using System.Runtime.CompilerServices;

public class Contest
{
	const long MOD1 = 1000000007L; // 10^9+7

	public static void Main()
	{
 
        int n, m;
		int[] s,t;
		MyIO.ReadMulti(out n, out m);
		MyIO.ReadArray(out s);
		MyIO.ReadArray(out t);

		CumulativeSum2D c = new CumulativeSum2D(n,m);
		if (s[0]==t[0]){
			c.Set(0,0,1);
		}else{
			c.Set(0,0,0);
		}
		for (int i = 1; i < m; i++) if (s[0]==t[i]){
			c.Set(0,i,1);
		}else{
			c.Set(0,i,0);
		}
		for (int i = 1; i < n; i++) if (s[i]==t[0]){
			c.Set(i,0,1);
		}else{
			c.Set(i,0,0);
		}
		for (int i = 1; i < n; i++)
		{
			for (int j = 1; j < m; j++)
			{
				long val= c.Area(0,0,i-1,j-1);
				if (s[i]==t[j]){
					c.Set(i,j,val+1);
				}else{
					c.Set(i,j,0);
				}


			}
		}



		MyIO.WriteMulti((c.Area(0,0,n-1,m-1)+1+MOD1)%MOD1);


 
		
	}









}




public class CumulativeSum2D
{
    public long[][] Values;

	public CumulativeSum2D(int sizeX, int sizeY){
		Values = new long[sizeX+1][];
		for(int i=0;i<=sizeX;i++) Values[i] = new long[sizeY+1];
	}
	public CumulativeSum2D(long[][] val) : this(val.Length, val[0].Length){
		for(int i=0;i<val.Length;i++) for(int j=0;j<val[i].Length;j++) Set(i, j, val[i][j]);
	}
	public void Set(int x, int y, long val){
		Values[x+1][y+1] = (val+Values[x][y+1]+Values[x+1][y]-Values[x][y])%1000000007L;
	}
	// 閉区間[x1:x2],[y1:y2]で囲まれた長方形エリアの累積和を計算
	public long Area(int x1, int y1, int x2, int y2){
		return (Values[x2+1][y2+1]-Values[x1][y2+1]-Values[x2+1][y1]+Values[x1][y1])%1000000007L;
	}

}






public struct VT<T, U>
{
	public T Item1; public U Item2;
    public VT(T a, U b) { Item1 = a; Item2 = b; }
}
public struct VT<T, U, V>
{
	public T Item1; public U Item2; public V Item3;
    public VT(T a, U b, V c) { Item1 = a; Item2 = b; Item3 = c; }
}
public struct VT<T, U, V, W>
{
	public T Item1; public U Item2; public V Item3; public W Item4;
    public VT(T a, U b, V c, W d) { Item1 = a; Item2 = b; Item3 = c; Item4 = d; }
}

public class Printer : System.IO.StreamWriter
{
	public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
	public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
}
public static class MyIO
{
	private static char[] splitter = new char[] {' '};
	private static bool eq<T, U>() => typeof(T).Equals(typeof(U));
	private static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
	private static T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
	                                  : eq<T, long>()   ? ct<T, long>(long.Parse(s))
	                                  : eq<T, double>() ? ct<T, double>(double.Parse(s, System.Globalization.CultureInfo.InvariantCulture))
	                                  : eq<T, char>()   ? ct<T, char>(s[0])
	                                                    : ct<T, string>(s);				
	public static string[] ReadMulti<T>(out T a) {
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(ar[0]);
		return ar;
	}
	public static string[] ReadMulti<T, U>(out T a, out U b) {
		var ar = ReadMulti<T>(out a); 
        b = cv<U>(ar[1]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V>(out T a, out U b, out V c) {
		var ar = ReadMulti<T, U>(out a, out b); 
        c = cv<V>(ar[2]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W>(out T a, out U b, out V c, out W d) {
		var ar = ReadMulti<T, U, V>(out a, out b, out c); 
        d = cv<W>(ar[3]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e) {
		var ar = ReadMulti<T, U, V, W>(out a, out b, out c, out d); 
        e = cv<X>(ar[4]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f) {
		var ar = ReadMulti<T, U, V, W, X>(out a, out b, out c, out d, out e); 
        f = cv<Y>(ar[5]);
		return ar;
	}
	public static string[] ReadArray<T>(out T[] a) {		
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries);
		a = ar.Select(cv<T>).ToArray();
		return ar;
	}		
	public static string[][] ReadLines<T>(int n, out T[] a) {
		a = new T[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadMulti(out a[i]);
		return arr;
	}
	public static string[][] ReadLines<T, U>(int n, out VT<T, U>[] a) {
		a = new VT<T, U>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p;
			arr[i] = ReadMulti(out o, out p);
			a[i] = new VT<T, U>(o, p);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V>(int n, out VT<T, U, V>[] a) {
		a = new VT<T, U, V>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q;
			arr[i] = ReadMulti(out o, out p, out q);
			a[i] = new VT<T, U, V>(o, p, q);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V, W>(int n, out VT<T, U, V, W>[] a) {
		a = new VT<T, U, V, W>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q; W r;
			arr[i] = ReadMulti(out o, out p, out q, out r);
			a[i] = new VT<T, U, V, W>(o, p, q, r);
		}
		return arr;
	}
	public static string[][] ReadMatrix<T>(int n, out T[][] a) {
		a = new T[n][];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadArray(out a[i]);
		return arr;
	}

	private static void wwp(Action act){
		var sw = new Printer(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	private static string wfm(Type t){
		return t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	}
	public static void WriteMulti(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length;i++) {
				string fs = wfm(a[i].GetType()) + ((i<a.Length-1) ? " " : Environment.NewLine);
				Console.Write(fs, a[i]);
			}
		});
	}
	public static void WriteArray<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T));
			string fs1 = fs + " ";
			string fs2 = fs + Environment.NewLine;
			for(int i=0;i<a.Length;i++) Console.Write( ((i<a.Length-1) ? fs1 : fs2), a[i]);
		});
	}
	public static void WriteLines<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T)) + Environment.NewLine;
			foreach(T x in a) Console.Write(fs, x);
		});
	}



}