The stocks of a company were valued at $N = 123456$ on day $0$. Every day for the following $M = 217127$ days, the value either rose by $1$ or decreased by $1$. Note that the value never remained the same. After $M$ days, the final value was observed to be $172213$.

Determine the number of distinct ways in which the stock value could have changed over the $M$ days, such that it never exceeded $L = 200000$.

Since the number of ways can be huge, print them modulo $10^9+7$.