20. Distribute $n+m$ distinct objects $a_{1}, a_{2}, \cdots, a_{n}, a_{n+1}, \cdots, a_{n+m}$ to $n$ people $A_{1}$, $A_{2}, \cdots, A_{n}$, such that each person gets at least one object and $a_{i}(i=1,2, \cdots, n)$ cannot be given to $A_{i}$. Let the number of different ways to distribute the objects be $l(n, m)$. Find the counting formula for $l(n, m)$.
20. $l(n, m)=\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(n-k-1)^{n-k}(n-k)^{m+k}$