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E - Common Subsequence /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

1 以上 10^5 以下の整数から成る、長さ N の整数列 S と 長さ M の整数列 T が与えられます。

S の部分列と T の部分列の組であって、整数列として等しいような組は何通りあるでしょうか。

ただし、整数列 A の部分列とは、A の要素を 0 個以上いくつか選んで削除し、残ったものを元の順序を保って並べた整数列を表します。

また、S, T それぞれの部分列は、整数列として等しい場合でも、削除した要素の添字の集合が異なる場合には異なる部分列として区別してください。

### 制約

• 1 \leq N, M \leq 2 \times 10^3
• S の長さは N である
• T の長さは M である
• 1 \leq S_i, T_i \leq 10^5
• 入力は全て整数である

### 入力

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


### 入力例 1

2 2
1 3
3 1


### 出力例 1

3


S の部分列としては (), (1), (3), (1, 3) が考えられます。

T の部分列としては (), (3), (1), (3, 1) が考えられます。

### 入力例 2

2 2
1 1
1 1


### 出力例 2

6


S の部分列としては (), (1), (1), (1, 1) が考えられます。

T の部分列としては (), (1), (1), (1, 1) が考えられます。

### 入力例 3

4 4
3 4 5 6
3 4 5 6


### 出力例 3

16


### 入力例 4

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


### 出力例 4

191


### 入力例 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


### 出力例 5

846527861


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.