3179 - Find the N-th Value After K Seconds\.

Medium

You are given two integers n and k.

Initially, you start with an array a of n integers where a[i] = 1 for all 0 <= i <= n - 1. After each second, you simultaneously update each element to be the sum of all its preceding elements plus the element itself. For example, after one second, a[0] remains the same, a[1] becomes a[0] + a[1], a[2] becomes a[0] + a[1] + a[2], and so on.

Return the value of a[n - 1] after k seconds.

Since the answer may be very large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: n = 4, k = 5

Output: 56

Explanation:

Example 2:

Input: n = 5, k = 3

Output: 35

Explanation:

Constraints:

• 1 <= n, k <= 1000