Let $f(n, m)$ count the number of sequences $(a_{1}, a_{2}, \cdots, a_{m})$ of length $m$ and $1 \le a_{i} \le n$, such that for each $1 \le i \le n, cnt(i) \le i$, where $cnt(i)$ is the number of times $i$ occurs in the sequence.

Find $f(50, 1000)$ mod $10^9 + 7$ .