Problem:
Score : 800 points

Problem Statement

12:17 (UTC): The sample input 1 and 2 were swapped. The error is now fixed. We are very sorry for your inconvenience.

There are N children in AtCoder Kindergarten, conveniently numbered 1 through N. Mr. Evi will distribute C indistinguishable candies to the children.

If child i is given a candies, the child's happiness will become x_i^a, where x_i is the child's excitement level. The activity level of the kindergarten is the product of the happiness of all the N children.

For each possible way to distribute C candies to the children by giving zero or more candies to each child, calculate the activity level of the kindergarten. Then, calculate the sum over all possible way to distribute C candies. This sum can be seen as a function of the children's excitement levels x_1,..,x_N, thus we call it f(x_1,..,x_N).

You are given integers A_i,B_i (1≦i≦N). Find modulo 10^9+7.

Constraints

1≦N≦400

1≦C≦400

1≦A_i≦B_i≦400 (1≦i≦N)

Partial Score

400 points will be awarded for passing the test set satisfying A_i=B_i (1≦i≦N).

Input

The input is given from Standard Input in the following format:

N C
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

Print the value of modulo 10^9+7.

Sample Input 1

2 3
1 1
1 1

Sample Output 1

4

This case is included in the test set for the partial score, since A_i=B_i.
We only have to consider the sum of the activity level of the kindergarten where the excitement level of both child 1 and child 2 are 1 (f(1,1)).

If child 1 is given 0 candy, and child 2 is given 3 candies, the activity level of the kindergarten is 1^0*1^3=1.

If child 1 is given 1 candy, and child 2 is given 2 candies, the activity level of the kindergarten is 1^1*1^2=1.

If child 1 is given 2 candies, and child 2 is given 1 candy, the activity level of the kindergarten is 1^2*1^1=1.

If child 1 is given 3 candies, and child 2 is given 0 candy, the activity level of the kindergarten is 1^3*1^0=1.

Thus, f(1,1)=1+1+1+1=4, and the sum over all f is also 4.

Sample Input 2

1 2
1
3

Sample Output 2

14

Since there is only one child, child 1's happiness itself will be the activity level of the kindergarten. Since the only possible way to distribute 2 candies is to give both candies to child 1, the activity level in this case will become the value of f.

When the excitement level of child 1 is 1, f(1)=1^2=1.

When the excitement level of child 1 is 2, f(2)=2^2=4.

When the excitement level of child 1 is 3, f(3)=3^2=9.

Thus, the answer is 1+4+9=14.

Sample Input 3

2 3
1 1
2 2

Sample Output 3

66

Since it can be seen that f(1,1)=4 , f(1,2)=15 , f(2,1)=15 , f(2,2)=32, the answer is 4+15+15+32=66.

Sample Input 4

4 8
3 1 4 1
3 1 4 1

Sample Output 4

421749

This case is included in the test set for the partial score.

Sample Input 5

3 100
7 6 5
9 9 9

Sample Output 5

139123417

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::iter::FromIterator;

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

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let n = scan.read::<usize>();
    let c = scan.read::<usize>();
    let a = scan.readn::<usize>(n);
    let b = scan.readn::<usize>(n);
    // powm[a][b] = b ^ a
    let mut powm = vecs![Co(1);404;404];
    for i in 1..401 {
        for j in 0..400 {
            powm[j+1][i] = powm[j][i] * i.into();
        }
    }
    let mut mcum = vec![];
    for i in 0..404 {
        mcum.push(Cum::new(&powm[i]));
    }
    let mut dp = vecs![Co(0);n+1;c+1];
    dp[0][0] = Co(1);
    for i in 0..n {
        for x in 0..c + 1 {
            for y in 0..c + 1 {
                if x + y > c {break;}
                dp[i+1][x+y] += dp[i][x] * mcum[y].sum(a[i]..b[i]+1);
            }
        }
    }
    println!("{}", dp[n][c]);
}

use std::ops::Range;

#[derive(Debug)]
#[allow(dead_code)]
struct Cum {
    s: Vec<Co>,
}


#[allow(dead_code)]
impl Cum {
    fn new(a: &Vec<Co>) -> Cum {
        let mut s = vec![Co(0); a.len() + 1];
        for i in 0..a.len() {
            s[i + 1] = s[i] + a[i];
        }
        Cum { s: s }
    }
    /// [l,r)
    fn sum(&self, range: Range<usize>) -> Co {
        self.s[range.end] - self.s[range.start]
    }
}

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

// region modulo
#[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: i64) -> 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)
    }
}

#[allow(dead_code)]
impl From<i32> for Co {
    fn from(value: i32) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl From<i64> for Co {
    fn from(value: i64) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl From<usize> for Co {
    fn from(value: usize) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl AddAssign for Co {
    fn add_assign(&mut self, other: Self) {
        *self = self.add(other);
    }
}
#[allow(dead_code)]
impl Add for Co {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        Co::from((self.0).add(other.0))
    }
}
#[allow(dead_code)]
impl SubAssign for Co {
    fn sub_assign(&mut self, other: Self) {
        *self = self.sub(other);
    }
}
#[allow(dead_code)]
impl Sub for Co {
    type Output = Self;
    fn sub(self, other: Self) -> Self {
        Co::from((self.0).sub(other.0))
    }
}
#[allow(dead_code)]
impl MulAssign for Co {
    fn mul_assign(&mut self, other: Self) {
        *self = self.mul(other);
    }
}
#[allow(dead_code)]
impl Mul for Co {
    type Output = Self;
    fn mul(self, other: Self) -> Self {
        Co::from((self.0).mul(other.0))
    }
}
#[allow(dead_code)]
impl DivAssign for Co {
    fn div_assign(&mut self, other: Self) {
        *self = self.div(other);
    }
}
#[allow(dead_code)]
impl Div for Co {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.pow((M - 2) as i64)
    }
}
// endregion

// region template
#[allow(dead_code)]
fn iu(i: i64) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> i64 { i as i64 }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

#[allow(dead_code)]
fn arr<'a, S, T>(n: usize, mut f: S) -> Vec<T> where S: FnMut(usize) -> T + 'a {
    (0..n).map(|i| f(i)).collect::<Vec<T>>()
}

#[allow(dead_code)]
fn alt<S, T>(v: Vec<S>) -> T where T: FromIterator<S> {
    v.into_iter().collect::<T>()
}

#[allow(dead_code)]
fn dup<S, T>(v: &[S]) -> T where T: FromIterator<S>, S: Clone {
    v.iter().cloned().collect::<T>()
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect()
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion