Octopus

Time limit1sMemory limit1024 MB

Summary

Starting from N vertices with no edges, find the most vertices that can each have exactly K incident edges in a simple undirected graph.

Level: Medium4 of 10
Topics: Math, Graph
Solved: No attempts yet

Problem

Graph $G$ starts with $N$ vertices and no edges. You may add undirected edges between two distinct vertices any number of times, but you cannot add a duplicate edge. Given $N$ , find the maximum number of octopus vertices that can be made by adding edges.

A vertex $V$ in a graph is called an octopus if exactly $K$ edges are connected to it.

Input

The first line contains $N$ and $K$ , separated by a space.

Output

On the first line, print the maximum number of octopus vertices that can be made by adding edges.

Constraints

$1 \le N, K \le 100\,000$

Examples2

Example 1
Input
```
4 3
```
Expected output
```
4
```
Example 2
Input
```
5 5
```
Expected output
```
0
```