Contest Duration: - (local time) (100 minutes) Back to Home
E - Children and Candies /

Time Limit: 4 sec / Memory Limit: 256 MB

### 制約

• 1≦N≦400
• 1≦C≦400
• 1≦A_i≦B_i≦400 (1≦i≦N)

### 部分点

• A_i=B_i (1≦i≦N) を満たすデータセットに正解した場合は、部分点として400 点が与えられる。

### 入力

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


### 出力

の値を10^9+7で割ったあまりを出力せよ。

### 入力例 1

2 3
1 1
1 1


### 出力例 1

4


A_i=B_iなので部分点の条件を満たします。 子供1,2はしゃぎ度が共に1のもの(f(1,1))を考えればよく、この時、

• 子供10個,子供23個のキャンディーをあげると、幼稚園の活発度1^0*1^3=1
• 子供11個,子供22個のキャンディーをあげると、幼稚園の活発度1^1*1^2=1
• 子供12個,子供21個のキャンディーをあげると、幼稚園の活発度1^2*1^1=1
• 子供13個,子供20個のキャンディーをあげると、幼稚園の活発度1^3*1^0=1

### 入力例 2

1 2
1
3


### 出力例 2

14


• 子供1はしゃぎ度1の時、f(1)=1^2=1
• 子供1はしゃぎ度2の時、f(2)=2^2=4
• 子供1はしゃぎ度3の時、f(3)=3^2=9

### 入力例 3

2 3
1 1
2 2


### 出力例 3

66


f(1,1)=4 , f(1,2)=15 , f(2,1)=15 , f(2,2)=32 となることがわかるので、答えは4+15+15+32=66になります。

### 入力例 4

4 8
3 1 4 1
3 1 4 1


### 出力例 4

421749


### 入力例 5

3 100
7 6 5
9 9 9


### 出力例 5

139123417


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