For a given number N you have K copies of each number from 1 to N. Therefore, you have a total of N*K numbers. You need to form M sets s1 ,s2 ,s3 , ....  sm  where a set should contain unique numbers(set may be empty).
Now, let D be the sum of size of all M sets.(where the size of a set is number of elements in it)
Let G(i)= number of ways to form M sets such that D is equal to i.
Find G(0)+ G(1) +...... G(N*K)  modulo 10^9 + 7.
Note: Ordering of sets matters as the sets are numbered.

For eg:
N=2, M=2, K=2
So, the numbers present initially are (1,1,2,2)
G(0)=1,     
{ } ,{ }

G(1)=4,
{1}, { }
{2},{ }
{ }, {1}
{ },{2}

G(2)=6,
{1},{2}
{2},{1}
{1},{1}
{2},{2}
{1,2} , { }
{ },{1,2}

G(3)=4,
{1,2},{1}
{1,2},{2}
{1}, {1,2}
{2}, {1,2}

G(4)=1,
{1,2}, {1,2}
{ } represents empty set.
So answer = G(0)+G(1)+G(2)+G(3)+G(4) = 16

Input Specification
First line of input consists of integer t denoting number of test cases.
Each of the next t lines contain 3 integers N, M , K where   N>=M>=K

Output Specification
Output consists of t lines. Each line contains the answer modulo 10^9 + 7.

 Constraint

 1<=t<=100
1<=M<=N<=100000
0<=K<=M

Sample Input
3
2 2 2
4 3 1
3 1 1
Sample Output
16
256
8