Problem:
Score : 200 points

Problem Statement

You are given two integers K and S.

Three variable X, Y and Z takes integer values satisfying 0≤X,Y,Z≤K.

How many different assignments of values to X, Y and Z are there such that X + Y + Z = S?

Constraints

2≤K≤2500

0≤S≤3K

K and S are integers.

Input

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

K S

Output

Print the number of the triples of X, Y and Z that satisfy the condition.

Sample Input 1

2 2

Sample Output 1

6

There are six triples of X, Y and Z that satisfy the condition:

X = 0, Y = 0, Z = 2

X = 0, Y = 2, Z = 0

X = 2, Y = 0, Z = 0

X = 0, Y = 1, Z = 1

X = 1, Y = 0, Z = 1

X = 1, Y = 1, Z = 0

Sample Input 2

5 15

Sample Output 2

1

The maximum value of X + Y + Z is 15, achieved by one triple of X, Y and Z.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <iostream>
#include <vector>
#include <utility>
#include <algorithm>

using namespace std;

int main(void) {
  int k, s;
  scanf("%d %d", &k, &s);

  int count = 0;

  for(int i = 0; i <= k; i++) {
    for(int j = i; j <= k; j++) {
      for(int l = j; l <= k; l++) {
	if(i + j + l == s) {
	  if( i == j && j == l) {
	    count++;
	  }
	  else if(i == j || j == l || l == i) {
	    count += 3;
	  }
	  else {
	    count += 6;
	  }
	}
      }
    }
  }
  printf("%d\n", count);
}