Tree and paths of length two

Time limit2sMemory limit512 MB

Summary

Decide whether some tree on N nodes has exactly S simple paths of length 2.

Level: Medium4 of 10
Topics: Tree, Combinatorics, Greedy
Solved: No attempts yet

Problem

Given $N$ and $S$ , write a program that decides whether a tree satisfying both of the following conditions exists.

The tree has $N$ nodes.
The number of simple paths of length 2 is $S$ .

A simple path is a path that does not pass through the same vertex more than once. The length of a path is the number of edges on it, so a simple path of length 2 joins three distinct vertices.

Direction does not matter in a path. A-B-C and C-B-A count as the same path.

Input

The first line contains $N$ and $S$ separated by a space. ( $1 \le N \le 50$ , $1 \le S \le 1000$ )

Output

Print 1 if such a tree can be built, and 0 if it cannot.

Examples4

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