Roses and pots (2)

You have roses of $c$ different colors. In particular, you have $n$ roses of each color. Please compute the number of ways to plant all the roses in a line of $cn$ pots, one rose per pot, in such a way that there is exactly one pair of adjacent roses of the same color. The roses of the same color are indistinguishable.

Input

Input consists of several cases, each with $c$ and $n$ . Assume that $c$ is either 2 or 3. For $c = 2$ , we have $1 \le n \le 10^7$ . For $c = 3$ , we have $1 \le n \le 200$ .

Output

For every case, print the answer modulo $10^8 + 7$ .

Problem information

Author: Salvador Roura

Generation: 2026-01-25T10:13:57.318Z