{ "data": { "question": { "questionId": "1263", "questionFrontendId": "1155", "boundTopicId": null, "title": "Number of Dice Rolls With Target Sum", "titleSlug": "number-of-dice-rolls-with-target-sum", "content": "

You have n dice and each die has k faces numbered from 1 to k.

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Given three integers n, k, and target, return the number of possible ways (out of the kn total ways) to roll the dice so the sum of the face-up numbers equals target. Since the answer may be too large, return it modulo 109 + 7.

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Example 1:

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\nInput: n = 1, k = 6, target = 3\nOutput: 1\nExplanation: You throw one die with 6 faces.\nThere is only one way to get a sum of 3.\n
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Example 2:

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\nInput: n = 2, k = 6, target = 7\nOutput: 6\nExplanation: You throw two dice, each with 6 faces.\nThere are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.\n
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Example 3:

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\nInput: n = 30, k = 30, target = 500\nOutput: 222616187\nExplanation: The answer must be returned modulo 109 + 7.\n
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Constraints:

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