Product of Array Except Self

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Given an array nums, return an array where each element is the product of all elements except itself. Do not use division.

Output space-separated.

Example

Input

1,2,3,4

Output

24 12 8 6

Reasoning

Input: nums is a list of integers, here 1,2,3,4. Each output position $i$ gets $\prod_{j \ne i} x_j$ , the product of every entry except $x_i$ .
Position 0 drops the $1$ : $2 \cdot 3 \cdot 4 = 24$ .
Position 1 drops the $2$ : $1 \cdot 3 \cdot 4 = 12$ .
Position 2 drops the $3$ : $1 \cdot 2 \cdot 4 = 8$ .
Position 3 drops the $4$ : $1 \cdot 2 \cdot 3 = 6$ .
Output: a list the same length as the input, printed space-separated as 24 12 8 6.
Notice why division is banned: with a zero in the input, as in $-1, 1, 0, -3, 3$ , every position except the zero's own includes that $0$ and becomes $0$ . Only the zero's position survives, at $(-1)(1)(-3)(3) = 9$ , giving 0 0 9 0 0. Dividing a total product by $x_i$ can't recover that $9$ .

Constraints

2 <= len(nums) <= 10^5
-30 <= nums[i] <= 30
The product of any prefix or suffix fits in a 32-bit integer

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solution.py

Python 3.13

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Product of Array Except Self

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