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: Accepted)

#include <stdio.h>

int main(){
    float x, y, x1, x2;
    int aux1, aux2;
    scanf("%f%f", &x, &y);

    float m[2][3] = {{1, 1, x}, {2, 4, y}};
    float k = m[1][0]/m[0][0];

    for(int i = 0; i < 2; i++){
        for(int j = 0; j < 3; j++){
            if(i == 1){
                m[1][j] = (m[1][j] - (k*m[0][j]));
            }
        }
    }

    x2 = m[1][2]/m[1][1];
    aux2 = x2;
    x1 = (m[0][2] - (m[0][1]*x2))/m[0][0];
    aux1 = x1;

    if(x2 == aux2 && x1 == aux1 && 4*x >= y && y >= 2*x){
        printf("Yes");
    }
    else{
        printf("No");
    }
    return 0;
}