MOON1 - Moon Safari (medium)

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Air is a music duo from France.
You will be told the secret of the critically acclaimed album Moon Safari: mathematics.
The goal of your new task is to compute an ethereal sum.

Three trips on the moon are provided, Moon (easy), Moon1 (medium), Moon2 (hard) with different constraints.

Input

The first line contains an integer T, the number of test cases.
On the next T lines, you will be given three integers N, a and r.

Output

Output T lines, one for each test case, with SN,a,r = sum( a^i i^r, for i in [1..N] ).
Since the answer can get very big, output it modulo 109+7.

Example

```Input:
2
3 4 5
6 7 8

Output:
16068
329990641
```

Explanation

The first case is, with N=3, a=4, r=5, about the sum : 4^1 × 1^5 + 4^2 × 2^5 + 4^3 × 3^5 = 4 + 512 + 15552 = 16068.
The second case is, with N=6, a=7, r=8, about the sum : 7^1 × 1^8 + 7^2 × 2^8 + 7^3 × 3^8 + 7^4 × 4^8 + 7^5 × 5^8 + 7^6 × 6^8 + 7^7 × 7^8 = 204329992069 ≡ 329990641 (mod 10^9+7).

Constraints

```1 < T
1 < r
1 < N < 10^9
1 < a < 10^9
(T < 1000 and r < 18 ) or (T < 100 and r < 72) or (T < 10 and r < 256) or (T = 1 and r < 444)
```

Information

This trip can be done with a O(T×r^2×log(N)) method and some interpreted languages.
My MOON1-Py3 code got AC in 9.00s for the 4 input files.
(My MOON2 code got AC in 0.00s with C, 0.18s with Py2.7, 0.35 with Py3.2)
Good luck and have fun ;-)