Creating sorted arrays

Let A[1..n] be an array of integers with \(n\) elements from \( \{ 1, 2, 3, \ldots, m \} \) such that A[1..n] is strictly increasing.

For numbers: \( n = 567 \) and \( m = 1933 \). If \( S \) is that actual number of different arrays, provide \( S \pmod {10^{9} + 7} \).


Example:

\( n = 2, m = 3 \): The format of required array is \(A[a_1, a_2]\); possible values for elements of array are from set \( \{1, 2, 3\} \). For this example, answer is \( \boxed{3} \). Arrays that suffice given conditions are:

  • \( A_1 = 1, 2 \)
  • \( A_2 = 2, 3 \)
  • \( A_3 = 1, 3 \)
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