Suppose that there are $N$ persons who are numbered $1, 2, ..., N$. Let there be $N$ hats, also numbered $1, 2, ..., N$. We have to find the number of ways in which no one gets the hat having same number as his/her number.

Let the number of ways to accomplish the above task be $D(N)$ . You need to enter the value of $D(N) mod P$.

Take $N$ = $49770435560715869$ and $P$ = $223092870$.