Score : $1000$ points

Problem Statement

Rng is baking cookies.

Initially, he can bake one cookie per second.

He can also eat the cookies baked by himself. When there are $x$ cookies not yet eaten, he can choose to eat all those cookies. After he finishes eating those cookies, the number of cookies he can bake per second becomes $x$. Note that a cookie always needs to be baked for $1$ second, that is, he cannot bake a cookie in $1/x$ seconds when $x > 1$. When he choose to eat the cookies, he must eat all of them; he cannot choose to eat only part of them. It takes him $A$ seconds to eat the cookies regardless of how many, during which no cookies can be baked.

He wants to give $N$ cookies to Grandma. Find the shortest time needed to produce at least $N$ cookies not yet eaten.

Constraints

• $1 \leq N \leq 10^{12}$
• $0 \leq A \leq 10^{12}$
• $A$ is an integer.

Partial Score

• $500$ points will be awarded for passing the test set satisfying $N \leq 10^6$ and $A \leq 10^6$.
• Additional $500$ points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

$N$ $A$

Output

Print the shortest time needed to produce at least $N$ cookies not yet eaten.

8 1

7

It is possible to produce $8$ cookies in $7$ seconds, as follows:

• After $1$ second: $1$ cookie is done.
• After $2$ seconds: $1$ more cookie is done, totaling $2$. Now, Rng starts eating those $2$ cookies.
• After $3$ seconds: He finishes eating the cookies, and he can now bake $2$ cookies per second.
• After $4$ seconds: $2$ cookies are done.
• After $5$ seconds: $2$ more cookies are done, totaling $4$.
• After $6$ seconds: $2$ more cookies are done, totaling $6$.
• After $7$ seconds: $2$ more cookies are done, totaling $8$.

1000000000000 1000000000000

1000000000000