\[X = \sum_{s=0}^{\min(n - m, k)} {n - m \choose s}^2 (s!) \sum_{x+y=k-s} {m \choose x}{n - m - s \choose x}{m \choose y}{n - m - s \choose y}(x!)(y!)
\]
\[Y = \sum_{L=0}^{\min(k,n-m)} {n - m \choose L}{m \choose L}L! {n - L \choose k - L}{n - m \choose k - L}(k - L)!
\]
求证 \(X = Y\)。