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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ECommonSubsequence solver = new ECommonSubsequence();
        solver.solve(1, in, out);
        out.close();
    }

    static class ECommonSubsequence {
        private NumberTheory.Mod107 mod = new NumberTheory.Mod107();

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt();
            int[] s = new int[n];
            for (int i = 0; i < n; i++)
                s[i] = in.nextInt();
            int[] t = new int[m];
            for (int i = 0; i < m; i++)
                t[i] = in.nextInt();

            NumberTheory.ModularNumber[][] answer = new NumberTheory.ModularNumber[n + 1][m + 1]; // answer[i][j] is the # nonempty using the first i chars and j chars

            for (int i = 0; i <= n; i++)
                for (int j = 0; j <= m; j++)
                    answer[i][j] = mod.create(0);

            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= m; j++) {
                    if (s[i - 1] == t[j - 1]) {
                        answer[i][j] = answer[i][j].add(answer[i - 1][j - 1]).add(1);
                    }
                    answer[i][j] = answer[i][j].add(answer[i - 1][j]);
                    answer[i][j] = answer[i][j].add(answer[i][j - 1]);
                    answer[i][j] = answer[i][j].subtract(answer[i - 1][j - 1]);
                }
            }

            out.println(answer[n][m].add(1));
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class NumberTheory {
        private static void ASSERT(boolean assertion) {
            if (!assertion)
                throw new AssertionError();
        }

        public abstract static class Modulus<M extends NumberTheory.Modulus<M>> {
            ArrayList<NumberTheory.ModularNumber<M>> factorial = new ArrayList<>();

            public abstract long modulus();

            public Modulus() {
                super();
                factorial.add(create(1));
            }

            public NumberTheory.ModularNumber<M> create(long value) {
                return new NumberTheory.ModularNumber(value, this);
            }

        }

        public static class Mod107 extends NumberTheory.Modulus<NumberTheory.Mod107> {
            public long modulus() {
                return 1_000_000_007L;
            }

        }

        public static class ModularNumber<M extends NumberTheory.Modulus<M>> {
            public final long value;
            public final M m;
            public final long MOD;

            public ModularNumber(long value, M m) {
                this.m = m;
                this.MOD = m.modulus();
                this.value = (value % MOD + MOD) % MOD;
            }

            public NumberTheory.ModularNumber<M> add(NumberTheory.ModularNumber<M> other) {
                ASSERT(m.modulus() == other.m.modulus());
                return this.add(other.value);
            }

            public NumberTheory.ModularNumber<M> add(long other) {
                return m.create(value + other);
            }

            public NumberTheory.ModularNumber<M> subtract(NumberTheory.ModularNumber<M> other) {
                ASSERT(m.modulus() == other.m.modulus());
                return this.subtract(other.value);
            }

            public NumberTheory.ModularNumber<M> subtract(long other) {
                return m.create(value - other);
            }

            public String toString() {
                return String.valueOf(value);
            }

        }

    }
}