Overclocking the GPUs

You are in charge of setting up a GPU cluster to train some ML models. Before beginning the hardware development, you want to overclock the GPUs to get maximal output.

To test out the maximal output, you’re given N identical GPUs.
You have access to an overclock function that goes from 0 to M

You can run an experiment by using a GPU with overclock(x) to see if the GPU works at overclock(x), or it gets destroyed rendering it unusable in future experiments. If the GPU survives an experiment you can use it on subsequent experiments.

Using these N GPUs you want to find the maximum value you can safely use in the overclocking function without destroying the GPU.

You also want to do this by executing the least number of experiments.

Given,

• N - number of GPUs
• M - maximum value for the overclock function

Find the minimum number of experiments you need to perform to find the maximum safe value for the overclock function.

Input Format

Two space seperated integers, N and M respectively

Output Format

A single integer indicating the answer

Constraints

• 1 \(\leq\) N \(\leq\) 10⁵
• 1 \(\leq\) M \(\leq\) 10⁹

Subtasks

1. (30 points)
   • 1 \(\leq\) N \(\leq\) 1000
   • 1 \(\leq\) M \(\leq\) 2000
2. (30 points)
   • 1 \(\leq\) N \(\leq\) 10³
   • 1 \(\leq\) M \(\leq\) 10⁴
3. (40 points)
   • No additional constraints.

Limits

• Time Limit: 1s
• Memory Limit: 256MB

Sample Input 0

1 2

Sample Output 0

2

Sample Input 1

3 4

Sample Output 1

3