Find the N-th Value After K Seconds

Start with a = [1, 1, ..., 1] of length n. Each second, update simultaneously:

a[i] := a[0] + a[1] + ... + a[i]

for all i. Return a[n-1] after k seconds, modulo 1_000_000_007.

Key fact: After k steps,

$$a[n-1] \;=\; \binom{n+k-1}{k} \;=\; \binom{n+k-1}{n-1}.$$

So compute a single binomial coefficient modulo $10^9+7$.