Problem:
Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

1 \leq X \leq 100

1 \leq Y \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8

Sample Output 1

Yes

The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100

Sample Output 2

No

There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2

Sample Output 3

Yes

We also consider the case in which there are only cranes or only turtles.

Solution in C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int main()
{
  int x, y;
  scanf("%d %d", &x, &y);
  
  if (y % 2 != 0) {
    // 足の数が奇数なら不可
    puts("No\n");
    return 0;
  }
  
  if (y > 4 * x) {
    // 全て鶴と仮定したときよりも足の数が多いのは不可
    puts("No\n");
    return 0;
  }
  
  if (y / 4 == x) {
    // 全て鶴にすることで可
    puts("Yes\n");
    return 0;
  }
  
  // 亀がx匹いると仮定し、足の数がそれより多ければ(4 - 2)で割り切れるかどうかで判定する
  int allTortoiseLegCount = 2 * x;
  int rest = y - allTortoiseLegCount;
  
  if (rest == 0) {
    // 全て亀にすることで可
    puts("Yes\n");
    return 0;
  }
  
  int craneCount = rest / 2;
  int tortoiseCount = x - craneCount;
  
  if (craneCount * 4 + tortoiseCount * 2 == y) {
    puts("Yes\n");
    return 0;
  }
  
  // 不可
  puts("No\n");
  
  return 0;
}