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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a);i<(LL)(b);i++)
#define REP(i,b) FOR(i,0,b)
#define ALL(c) c.begin(),c.end()
#define PB push_back
#define cat 
using namespace std;
typedef long long LL;
typedef double ld;
typedef int ut;
typedef vector<ut> VI;
typedef pair<ut,ut> pr;
typedef pair<ut,pr> ppr;
typedef vector<pr> Vpr;
typedef priority_queue<pr,Vpr,greater<pr> > PQ;
const int INF=1<<30;
const int BITSIZE=1<<17;
const LL p=7+1e9;
const int SIZE=401;
LL N,C;
LL A[SIZE],B[SIZE];
LL DP[SIZE][SIZE];
LL timer[SIZE][SIZE];
LL power(LL x,LL r){
	if(r&1) return x*power(x,r-1)%p;
	if(r==0) return 1;
	LL ans=power(x,r/2);
	return ans*ans%p; 
}
LL timesSum(int n,int c){
	if(timer[n][c]) return timer[n][c];
	if(n==0) return 0;
	return timer[n][c]=(power(n,c)+timesSum(n-1,c))%p;
}
LL gets(int x,int c){
	return (timesSum(B[x],c)-timesSum(A[x]-1,c)+p)%p;
}
LL solve(int n,int c){
	if(DP[n][c]) return DP[n][c];
	if(n==0) return c==0;
	if(c==-1) return 0;
	REP(i,c+1)
		DP[n][c]+=(solve(n-1,c-i)*gets(n,i))%p;
	
	return DP[n][c]%p;
}
int main(){
	cin >> N >> C;
	FOR(i,1,N+1) cin >> A[i];
	FOR(j,1,N+1) cin >> B[j];
	cout << solve(N,C) << endl;
	return 0;
}