Problem

To celebrate the anniversary of Googleland, N couples are going to go for a boat ride in a rowboat. The rowboat is very long, but it is only one person wide, so the people will sit in a line from front to back.

However, during a rehearsal of the voyage, the boat did not move! After investigating, the organizers found that some newlywed couples were not rowing, but writing love poems for each other the whole time. Specifically, there are M pairs of newlywed couples. If the two members of a newlywed couple are sitting next to each other, they will be so busy writing poems that they will not row.

Now the organizers have come to you, the smartest person in Googleland, to ask, how many possible ways are there to arrange all 2N people on the rowboat, such that for each of the M newlywed couples, the two members are not sitting next to each other? Two ways are different if there is some position in the boat at which the two ways use different people. Notice that for the purpose of counting the number of ways, the two members of a couple are not considered to be interchangeable. Since the number can be very large, the organizers only want to know the value of the answer modulo 1000000007(109+7).
Input

The first line of the input gives the number of test cases, T. T test cases follow. Each test case consists of one line with two integers N and M as described above.
Output

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the number of possible arrangements, modulo 1000000007(109+7).
Limits

1 ≤ T ≤ 100.
Small dataset

1 ≤ M ≤ N ≤ 100.
Large dataset

1 ≤ M ≤ N ≤ 100000.
Sample

Input
5
2 1
2 2
3 1
3 2
10 5

Output
Case #1: 12
Case #2: 8
Case #3: 480
Case #4: 336
Case #5: 560963525

In Sample Case #1, there are 2 couples. To make the description simpler, we use the characters A and a to represent the newlywed couple, and B and b to represent the other couple. Per the rules of the problem, A and a cannot be adjacent. There are 12 ways to arrange the four people:
ABab ABba AbaB AbBa
aBAb aBbA abAB abBA
BAba BabA bABa baBA

In Sample Case #2, both two couples are newlywed couples, so A and a cannot be adjacent, and B and b cannot be adjacent. They can be arranged in the following 8 ways:
ABab AbaB aBAb abAB
BAba BabA bABa baBA

import math
def c(m,n):
    a = math.factorial(m)//math.factorial(n)
    return a//math.factorial(m-n)

t = int(input())
for case in range(t):
    [n,m] = input().split(' ')
    n = int(n)
    m = int(m)
    l = 2*n
    count = 0
    flag = -1
    for i in range(m+1):
        flag = -flag
        a = c(m,i)
        b = math.factorial(l-i)
        d = 2**(i)
        count += a*b*d*flag
        # print(a,b,d,count,flag)
        # if count<0:
        #     print(count)
        # (_,count) = divmod(count,1000000007)
    (_, count) = divmod(count, 1000000007)
    print("Case #",end='')
    print(case+1,end='')
    print(": ",end='')
    print(count)

這道題花了兩個小時。。因為真心有點麻煩，只通過了small的沒有通過large的。
理解題意不難，輸入是兩個數字，前一個數字代表有多少對couple，比如2代表是AaBb兩對夫婦，然後第二個數字代表有多少對鬧矛盾的夫婦。鬧矛盾的夫婦是不可以坐在一起的不然他們只會打架就不來划船了。然後讓你算有多少組方法。
這道題放在高中就是一個難一點的排列組合問題嘛。。
搜了一下，這種題目是有公式的，代公式嘛，我尋思這時間複雜度也不高啊，難道是計算很耗時嗎。（那也只能是計算很耗時了）。總之大資料集沒有跑出來。