Chopsticks

Time limit1sMemory limit512 MB

Summary

Given N kinds of chopsticks in unlimited supply, find how many must be drawn to guarantee R pairs in the worst case.

Level: Easy3 of 10
Topics: Math, Combinatorics, Greedy, Implementation
Solved: No attempts yet

Problem

A chopstick holder contains $N$ kinds of chopsticks, with plenty of each kind. You draw chopsticks at random from this holder and must form $R$ pairs. In the worst case, how many chopsticks must you draw?

Input

Two integers $N, R$ are given. $(1 ≤ N,R ≤ 10^{18})$

Output

Print the number of chopsticks that must be drawn in the worst case.

Examples1

Example 1
Input
```
2 1
```
Expected output
```
3
```