You are given two integers, k and x.

The price of a positive integer num is defined as the number of set bits (bits with value $1$) in its binary representation at $1$ based indices from the right (least significant bit) that are multiples of x. That is, a bit at position $i$ ($1$ indexed from the right) contributes to the price of num if and only if $i \pmod x = 0$ and the $i$-th bit is $1$.

Return the maximum integer num such that the sum of the prices of all integers from $1$ to num is less than or equal to k.

Constraints:

• $1 \leq$ k $\leq 10^{15}$

• $1 \leq$ x $\leq 8$

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