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-----
2 3
1 1
1 1

-----Sample Output-----
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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def main(N,C,A,B):\n    import sys\n    input = sys.stdin.readline\n    #N,C = map(int,input().split())\n    #A = list(map(int,input().split()))\n    #B = list(map(int,input().split()))\n    mod = 10**9+7\n    powA = [[0]*(401) for i in range(401)]\n    for i in range(401):\n        for j in range(401):\n            powA[i][j] = pow(i,j,mod)\n    \n    S = [[0]*401 for i in range(C+1)]\n    for i in range(C+1):\n        S[i][0] = 0\n    for i in range(C+1):\n        for j in range(1,401):\n            S[i][j] = (S[i][j-1] + powA[j][i])%mod\n    \n    dp = [[0]*(C+1) for i in range(N)]\n    for i in range(C+1):\n        dp[0][i] = S[i][B[0]] - S[i][A[0]-1]\n    for i in range(1,N):\n        for j in range(C+1):\n            tmp = 0\n            for k in range(j+1):\n                tmp = (tmp + (S[k][B[i]] - S[k][A[i]-1])*dp[i-1][j-k])%mod\n            dp[i][j] = tmp\n    print(dp[N-1][C])\n    #print(S[1])\n    \ndef main2(N,C,A,B):\n    import sys\n    input = sys.stdin.readline\n    #N,C = map(int,input().split())\n    #A = list(map(int,input().split()))\n    #B = list(map(int,input().split()))\n    mod = 10**9+7\n    powA = [[0]*(401) for i in range(401)]\n    for i in range(401):\n        for j in range(401):\n            powA[i][j] = pow(i,j,mod)\n    \n    S = [[0]*400 for i in range(C+1)]\n    for i in range(C+1):\n        S[i][0] = 1\n    for i in range(C+1):\n        for j in range(1,400):\n            S[i][j] = (S[i][j-1] + powA[j+1][i])%mod\n    \n    dp = [[0]*(C+1) for i in range(N)]\n    for i in range(C+1):\n        dp[0][i] = pow(A[0],i,mod)\n    for i in range(1,N):\n        for j in range(C+1):\n            tmp = 0\n            for k in range(j+1):\n                tmp = (tmp + powA[A[i]][k]*dp[i-1][j-k])%mod\n            dp[i][j] = tmp\n    print(dp[N-1][C])\n    \nimport sys\ninput = sys.stdin.readline\nN,C = map(int,input().split())\nA = list(map(int,input().split()))\nB = list(map(int,input().split()))\n\nif A==B:\n    main2(N,C,A,B)\nelse:\n    main(N,C,A,B)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 6473263