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 109 + 7.
\n
Example 1:
\n\nInput: n = 4, k = 5
\n\nOutput: 56
\n\nExplanation:
\n\n| Second | \n\t\t\tState After | \n\t\t
|---|---|
| 0 | \n\t\t\t[1,1,1,1] | \n\t\t
| 1 | \n\t\t\t[1,2,3,4] | \n\t\t
| 2 | \n\t\t\t[1,3,6,10] | \n\t\t
| 3 | \n\t\t\t[1,4,10,20] | \n\t\t
| 4 | \n\t\t\t[1,5,15,35] | \n\t\t
| 5 | \n\t\t\t[1,6,21,56] | \n\t\t
Example 2:
\n\nInput: n = 5, k = 3
\n\nOutput: 35
\n\nExplanation:
\n\n| Second | \n\t\t\tState After | \n\t\t
|---|---|
| 0 | \n\t\t\t[1,1,1,1,1] | \n\t\t
| 1 | \n\t\t\t[1,2,3,4,5] | \n\t\t
| 2 | \n\t\t\t[1,3,6,10,15] | \n\t\t
| 3 | \n\t\t\t[1,4,10,20,35] | \n\t\t
\n
Constraints:
\n\n1 <= n, k <= 1000nums, k times."
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