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)

/*------------------------------------------------------------------*/
/*------------------------- begin template -------------------------*/
/*------------------------------------------------------------------*/

// ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
// diff: using Parser
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

use std::io;
use std::io::BufRead;
use std::str;

// ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
// ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
// diff: using std::io::BufRead::fill_buf()
pub struct Parser<R> {
    pub reader: R,
    buf: Vec<u8>,
    pos: usize,
}

impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}

impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
    pub fn fast_i64(&mut self) -> i64 {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            if begin == self.buf.len() {
                self.update_buf();
                continue;
            }
            let mut res = 0;
            let (is_positive, mut end) = match self.buf[begin] {
                b'+' => (true, begin + 1),
                b'-' => (false, begin + 1),
                _ => (true, begin),
            };
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return if is_positive { res } else { -res };
            } else {
                self.update_buf();
            }
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;
use std::marker::PhantomData;
use std::ops::*;

pub trait ModP {
    fn as_u64() -> u64;
}

#[allow(non_camel_case_types)]
#[derive(Clone, Copy, Debug)]
pub struct Mod_1_000_000_007();
impl ModP for Mod_1_000_000_007 {
    fn as_u64() -> u64 {
        1_000_000_007
    }
}

#[allow(non_camel_case_types)]
#[derive(Clone, Copy, Debug)]
pub struct Mod_998_244_353();
impl ModP for Mod_998_244_353 {
    fn as_u64() -> u64 {
        998_244_353
    }
}

#[derive(Clone, Copy, PartialEq, Debug)]
pub struct Modular<P: ModP + Copy>(u32, PhantomData<P>);

impl<P: ModP + Copy> Modular<P> {
    pub fn new(x: u32) -> Modular<P> {
        Modular((x as u64 % P::as_u64()) as u32, PhantomData)
    }
    pub fn pow(self, n: u64) -> Modular<P> {
        if n == 0 {
            return Modular(1, PhantomData);
        }
        let t = self.pow(n / 2);
        if n % 2 == 0 {
            t * t
        } else {
            t * t * self
        }
    }
    pub fn as_u32(self) -> u32 {
        self.0
    }
}

impl<P: ModP + Copy> Add for Modular<P> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        let t = (self.0 + rhs.0) as u64;
        let u = if t < P::as_u64() { t } else { t - P::as_u64() };
        Modular(u as u32, PhantomData)
    }
}

impl<P: ModP + Copy> AddAssign for Modular<P> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<P: ModP + Copy> Sub for Modular<P> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        let t = if self.0 >= rhs.0 {
            self.0 as u64 - rhs.0 as u64
        } else {
            self.0 as u64 + P::as_u64() - rhs.0 as u64
        };
        assert!(t < P::as_u64());
        Modular(t as u32, PhantomData)
    }
}

impl<P: ModP + Copy> SubAssign for Modular<P> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<P: ModP + Copy> Neg for Modular<P> {
    type Output = Modular<P>;
    fn neg(self) -> Modular<P> {
        Modular((P::as_u64() - self.0 as u64) as u32, PhantomData)
    }
}

impl<P: ModP + Copy> Mul for Modular<P> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        Modular(
            ((self.0 as u64 % P::as_u64()) * (rhs.0 as u64 % P::as_u64()) % P::as_u64()) as u32,
            PhantomData,
        )
    }
}

impl<P: ModP + Copy> MulAssign for Modular<P> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<P: ModP + Copy> Div for Modular<P> {
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        if rhs.0 == 0 {
            loop {}
        }
        assert!(rhs.0 != 0);
        self * rhs.pow(P::as_u64() - 2)
    }
}

pub fn gen_fact_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
    let mut res = vec![Modular::<P>::new(1); n + 1];
    for i in 0..n {
        res[i + 1] = res[i] * Modular::<P>::new((i + 1) as u32);
    }
    res
}

pub fn gen_inv_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
    let mut res = vec![Modular::<P>::new(0); n + 1];
    res[1] = Modular::<P>::new(1);
    for i in 2..n + 1 {
        res[i] =
            -res[P::as_u64() as usize % i] * Modular::<P>::new((P::as_u64() / i as u64) as u32);
    }
    res
}

fn main() {
    input! {
        new_stdin_parser = parser,
    }
    let res = solve(&mut parser);
    print!("{}", res);
}

/*------------------------------------------------------------------*/
/*-------------------------- end template --------------------------*/
/*------------------------------------------------------------------*/

type Mod = Modular<Mod_1_000_000_007>;

use std::fmt::Write;
fn solve<R: BufRead>(parser: &mut Parser<R>) -> String {
    let mut buf = String::new();
    input! {
        parser = parser,
        n: usize,
        m: usize,
        xs: [i64; n],
        ys: [i64; m],
    }
    let mut dp = vec![vec![Mod::new(0); m + 1]; n + 1];
    dp[0][0] = Mod::new(1);
    for i in 0..n + 1 {
        for k in 0..m + 1 {
            if i > 0 {
                dp[i][k] += dp[i - 1][k];
            }
            if k > 0 {
                dp[i][k] += dp[i][k - 1];
            }
            if i > 0 && k > 0 {
                dp[i][k] -= dp[i - 1][k - 1];
            }
            if i > 0 && k > 0 && xs[i - 1] == ys[k - 1] {
                dp[i][k] += dp[i - 1][k - 1];
            }
        }
    }
    // eprintln!("{:?}", dp);
    writeln!(buf, "{}", dp[n][m].as_u32());
    buf
}