Full Moon Day

In a galaxy far, far away, there’s a planet named Planet-X. This planet has M months per year and D days per month. However, unlike planet Earth it has N number of moons. Each moon takes a different number of days (X_n) to orbit Planet-X. So, on this planet a day is called a Full Moon day, if all the moons get its lunar phase as Full Moon on that day. ( A lunar phase of a moon is the shape of the sunlit portion of the moon i.e. the visible portion of the moon )

Given a date of a full moon day(D₁), your task is to find whether the 2nd date(D₂) is a full moon day. If it’s not a full moon day, find C, the number of days to the closest full moon day.

Input Format

First line contains 3 integers, M, D & N.
Next line contains N integers, X₁, X₂, …, X_n
Next line contains 3 integers, y₁, m₁, d₁. The year, month and date of D₁ respectively.
Last line contains 3 integers, y₂, m₂, d₂. The year, month and date of D₂ respectively.

Output Format

If D₂ is a Full Moon Day, print “FULL MOON DAY”.
If not, print a single positive integer C, the number of days to the closest full moon day.

Constraints

If the number of days between D1 & D2 is Z,

• 1 \(\leq\) M, D \(\leq\) 10⁴
• 1 \(\leq\) N \(\leq\) 10²
• 1 \(\leq\) X_n \(\leq\) M * 3
• 1 \(\leq\) Z \(\leq\) 10⁸
• 1 \(\leq\) y₁, y₂ \(\leq\) 10⁸
• 1 \(\leq\) m₁, m₂ \(\leq\) M
• 1 \(\leq\) d₁, d₂ \(\leq\) D  

Limits

• Time Limit: 1s
• Memory Limit: 256MB

Sample Input 0

12 30 1
28
2019 12 10
2020 1 8

Sample Output 0

FULL MOON DAY

Sample Input 1

5 10 2
2 3
2019 1 1
2019 2 2

Sample Output 1

1