#P9564. Dice Throw Verification

    ID: 22711 Type: Default 1000ms 256MiB

Dice Throw Verification

Dice Throw Verification

Dice are small, throwable objects with marked sides, typically used to produce random values in tabletop games. A common die is a cube with faces numbered from $1$ to $6$, where each face shows a pattern of $n$ round dots (called pips) for face $n$. In these dice, the pips on faces $1$ and $4$ are colored red, while the pips on faces $2$, $3$, $5$, and $6$ are black.

Little Cyan Fish claims that when he threw three dice, the total number of red pips facing up was exactly A and the total number of black pips facing up was exactly B. Your task is to verify whether it is possible to throw three dice so that the sum of the red pips equals $A$ and the sum of the black pips equals $B$.

Note: Each die has the following faces:

  • Face 1: red=1, black=0
  • Face 2: red=0, black=2
  • Face 3: red=0, black=3
  • Face 4: red=4, black=0
  • Face 5: red=0, black=5
  • Face 6: red=0, black=6

inputFormat

The input consists of a single line containing two integers A and B separated by space, where:

  • A denotes the total number of red pips observed.
  • B denotes the total number of black pips observed.

outputFormat

Output a single line: YES if it is possible to throw three dice such that the total red pips equal A and the total black pips equal B; otherwise, output NO.

sample

2 6
YES