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Number of Dice Rolls With Target Sum

Bloomberg LP● MediumNEW GRADONSITE INTERVIEW

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Problem statement

Roll dice identical dice, each with faces numbered from 1 through faces. Return the number of ordered outcomes whose sum equals target, modulo 1,000,000,007.

Function

numRollsToTarget(dice: int, faces: int, target: int) → int

Examples

Example 1

dice = 2faces = 6target = 7return = 6

The ordered pairs are (1,6) through (6,1).

Constraints

1 <= dice, faces <= 30.
1 <= target <= 1000.