Find the N-th Value After K Seconds

Starting from an array of n ones, apply k rounds of replacing each element by the prefix sum up to that index and return a[n-1] modulo 1e9+7. Key insight: the value equals the binomial coefficient C(n+k-1, k), so the problem reduces to computing that combination mod 1e9+7 (n,k ≤ 1000).