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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"log"
	"os"
	"strconv"
)

func main() {
	x := readInt64() // count of animals
	y := readInt64() // count of legs

	turu := int64(2)
	kame := int64(4)
	deltaTuruKame := kame - turu

	allTuruLegs := x * turu
	allKameLegs := x * kame

	delta := y - allTuruLegs

	if delta < 0 {
		fmt.Println("No")
		return
	}

	//奇数
	if y%2 != 0 {
		fmt.Println("No")
		return
	}

	//鶴のみ
	if delta == 0 {
		fmt.Println("Yes")
		return
	}

	//亀のみ
	if y-allKameLegs == 0 {
		fmt.Println("Yes")
		return
	}

	countOfSwap := delta / deltaTuruKame

	if countOfSwap > x {
		fmt.Println("No")
		return
	}

	if kame*countOfSwap+turu*(x-countOfSwap) == y {
		fmt.Println("Yes")
		return
	} else {
		fmt.Println("No")
		return
	}
}

var (
	scanner *bufio.Scanner
)

func init() {
	scanner = bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
}

func readInt64() int64 {
	var t string

	if scanner.Scan() {
		t = scanner.Text()
	}

	n, err := strconv.ParseInt(t, 10, 64)
	if err != nil {
		log.Fatal(err)
	}

	return n

}