Harshikaa and the Rain RAINDROPS

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Tracy is teaching Charlie maths via a game called $N$-Cube, which involves three sections involving $N$.

Tracy gives Charlie a number $N$, and Charlie makes a list of $N$-th powers of integers in increasing order $1^N,2^N,3^N,\dot{,}\text{so on}$. This teaches him exponentiation.

Then Charlie performs the following subtraction game $N$ times: Take all pairs of consecutive numbers in the list and take their difference. These differences then form the new list for the next iteration of the game. Eg, if $N$ was 6, the list proceeds as $[1,64,729,4096\dots ]$ to $[63,685,3367\dots ]$, and so on $5$ more times.

After the subtraction game, Charlie has to correctly tell Tracy the $N$-th element of the list. This number is the value of the game.

After practice Charlie became an expert in the game. To challenge him more, Tracy will give two numbers $M$ (where $M$ is a prime) and $R$ instead of just a single number $N$, and the game must start from $M_R-1$ instead of $N$. Since the value of the game can now become large, Charlie just have to tell the largest integer $K$ such that $M_K$ divides this number. Since even $K$ can be large, output $K$ modulo 1000000007 (${10}^9+7$).