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Minimum Operations to Make the Integer Zero

You are given two integers num1 and num2.

You are given two integers num1 and num2.

In one operation, you can choose integer i in the range [0, 60] and subtract 2i + num2 from num1.

Return the integer denoting the minimum number of operations needed to make num1 equal to 0.

If it is impossible to make num1 equal to 0, return -1.

Example 1

Input: num1 = 3, num2 = -2

Output: 3

Explanation: We can make 3 equal to 0 with the following operations: - We choose i = 2 and subtract 22 + (-2) from 3, 3 - (4 + (-2)) = 1. - We choose i = 2 and subtract 22 + (-2) from 1, 1 - (4 + (-2)) = -1. - We choose i = 0 and subtract 20 + (-2) from -1, (-1) - (1 + (-2)) = 0. It can be proven, that 3 is the minimum number of operations that we need to perform.

Example 2

Input: num1 = 5, num2 = 7

Output: -1

Explanation: It can be proven, that it is impossible to make 5 equal to 0 with the given operation.

Constraints

  • 1 <= num1 <= 10^9
  • -10^9 <= num2 <= 10^9

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