Sonic And K - Separated Elements

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Sonic has an array of natural numbers from $1$ to $N$. He selects $M$ elements from the array. Now Sonic is satisfied only if the difference between all pair of elements is at least $K$. He is interested to find the number of ways of picking such $M$ elements which make him satisfied. Help him calculate the same. As the number of ways can be large output the answer modulo $10 ^ 9 + 7$. ###Input:

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solution.cppC++17

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