Find the Count of Monotonic Pairs I

Count the number of pairs of nonnegative integer sequences arr1 (non-decreasing) and arr2 (non-increasing) of length n such that arr1[i] + arr2[i] = nums[i] for all i, returning the result modulo 10^9+7. The core challenge is to count valid per-index value splits under the global monotonicity constraints (n ≤ 2000, nums[i] ≤ 50), typically solved with DP/combinatorics across positions.