Function Counting

Time Limit: 4000/2000 MS (Java/Others)

Memory Limit: 153428/153428 K (Java/Others)

Description

In this problem, we count the number of function f(x) satisfies below details.
1.f: M→M, ( M={-n,-n+1,-n+2,…,-1,0,1,…,n} )
2.$\forall x∈M, f_k (x)= -x,( f_0 (x)=x,f_i= f(f_{i-1} ) (i= 1,2,…) )$
3.$\forall x∈M, |(|f(x)|-|x|)|≤2$

Input

The first line of input contains an integer T (1 <= T <= 100) , the number of test cases.
Each test case contains a pair of integers n, k (n * k <= $10^9$), the upper limit of the set M and degree of f.
The total sum of n * k over all test cases does not exceed 4e9.

Output

For each test case output the answer % 1000000007.

Sample Input

7 1 1 2 1 100 1 1 2 2 2 3 2 20 4

Sample Output

1 1 1 0 2 0 1048576
Hint
If k = 1, only one function f(x) = -x exists. If n = k = 2, two functions exist. f: (-2, -1, 0, 1, 2) -> (1, -2, 0, 2, -1) or (-1, 2, 0, -2, 1).

Hint

liuyiding

Source

2017 Multi-University Training Contest - Te

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