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Number of Sub-arrays With Odd Sum

Given an array of integers arr, return the number of subarrays with an odd sum.

Given an array of integers arr, return the number of subarrays with an odd sum.

Since the answer can be very large, return it modulo 10^9 + 7.

Number of Sub-arrays With Odd Sum diagram

Example 1

Input: arr = [1,3,5]

Output: 4

Explanation: All subarrays are [[1],[1,3],[1,3,5],[3],[3,5],[5]] All sub-arrays sum are [1,4,9,3,8,5]. Odd sums are [1,9,3,5] so the answer is 4.

Example 2

Input: arr = [2,4,6]

Output: 0

Explanation: All subarrays are [[2],[2,4],[2,4,6],[4],[4,6],[6]] All sub-arrays sum are [2,6,12,4,10,6]. All sub-arrays have even sum and the answer is 0.

Example 3

Input: arr = [1,2,3,4,5,6,7]

Output: 16

Constraints

  • 1 <= arr.length <= 10^5
  • 1 <= arr[i] <= 100

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