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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_macros)]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! input_inner { ( $ next : expr ) => { } ; ( $ next : expr , ) => { } ; ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! read_value { ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) } ; ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 } ; ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) } ; }

#[allow(unused_macros)]
macro_rules ! vec_md { ( $ init : expr ; $ ( $ dim : expr ) ;* ) => { vec_md ! ( $ ( $ dim ) ;* => $ init ) } ; ( $ head : expr ; $ ( $ tail : expr ) ;* => $ init : expr ) => { vec ! [ vec_md ! ( $ ( $ tail ) ;* => $ init ) ; $ head ] } ; ( $ head : expr => $ init : expr ) => { vec ! [ $ init ; $ head ] } ; }

fn main() {
    input! {
        n: usize, m: usize,
        s: [u64;n],
        t: [u64;m]
    }

    let mut dp0 = vec_md![Co(0);n+1;m+1];
    let mut dp1 = vec_md![Co(0);n+1;m+1];
    dp0[0][0] = Co(1);
    for i in 0..dp0.len() {
        for j in 0..dp0[0].len() {
            if i+1 < dp0.len() {
                dp0[i+1][j] += dp0[i][j];
            }
            dp1[i][j] += dp0[i][j];
            if j+1 < dp0[0].len() {
                dp1[i][j+1] += dp1[i][j];
            }
            if i<n && j<m && s[i] == t[j] {
                dp0[i+1][j+1] += dp1[i][j];
            }
        }
    }
    println!("{}", dp1[n][m]);
}

#[allow(dead_code)]
const M: i64 = 1_000_000_007;

#[allow(dead_code)]
use std::ops::*;
#[allow(dead_code)]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct Co(pub i64);
#[allow(dead_code)]
impl Co {
    pub fn pow(self, mut n: u64) -> Self {
        let mut a = self;
        let mut res = Co(1);
        while n > 0 {
            if n & 1 == 1 {
                res *= a;
            }
            a = a * a;
            n >>= 1;
        }
        res
    }
}
#[allow(dead_code)]
impl std::fmt::Display for Co {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
macro_rules ! impl_from { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl From <$ tpe > for Co { fn from ( value : $ tpe ) -> Self { Co ( ( value as i64 % M + M ) % M ) } } ) * } }
impl_from!(i64, u64, usize);
macro_rules ! impl_binop { ( $ op : ident ,$ atr : ident ,$ assign : ident $ ( ,$ optr : ident ) * ) => { impl $ atr for Co { fn $ assign ( & mut self , other : Self ) { * self = self .$ op ( other ) ; } } $ ( impl $ optr for Co { type Output = Self ; fn $ op ( self , other : Self ) -> Self { Co :: from ( ( self . 0 ) .$ op ( other . 0 ) ) } } ) * } }
impl_binop!(add, AddAssign, add_assign, Add);
impl_binop!(sub, SubAssign, sub_assign, Sub);
impl_binop!(mul, MulAssign, mul_assign, Mul);
impl_binop!(div, DivAssign, div_assign);
#[allow(dead_code)]
impl Div for Co {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.pow((M - 2) as u64)
    }
}