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>
#include <string.h>

#define rep(i, n) for (int i = 0; i < n; i = i + 1)
#define MAX 10010
#define MAX_INT 9223372036854775807

int main() {
  // n: 亀の数
  // X - n: 鶴の数
  long long n = 0;

  char output[4] = "No";
  short X, Y;
  scanf("%hd%hd", &X, &Y);

  // 全部鶴のパターンからはじめ
  // 亀を一匹ずつ増やと同時に鶴を一匹ずつ減らす
  // 鶴が0匹になるまで続ける
  while(X - n >= 0) {
    // 鶴と亀の足を合計した数がYになったら終了
    if ((4 * n) + (2 * (X - n)) == Y) {
      strcpy(output, "Yes");
      break;
    }
    n += 1;
  }

  printf("%s\n", output);
  return 0;
}