MBINGO - Bingo!

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Albert, Charles and Mary invented a new version of the classical game Bingo. In traditional
Bingo the game is presided over by a non-player known as the caller. At the beginning of the
game each player is given a card containing a unique combination of numbers from 0 to N
arranged in columns and rows. The caller has a bag containing N + 1 balls, numbered from 0
to N. On each turn, the caller randomly selects a ball from the bag, announces the number of
the drawn ball to the players, and sets the ball aside so that it cannot be selected again. Each
player searches his card for the called number and marks it if he finds it. The first player who
marks a complete pre-announced pattern on the card (for example, a full horizontal line) wins
a prize.
In the Albert-Charles-Mary version, on each turn, the caller draws a first ball, returns it to
the bag, draws a second ball, returns it to the bag, and then calls out the absolute difference
between the two ball numbers. To generate even more excitement, before the game started a
possibly empty subset of balls is removed from the bag, in such a way that at least two balls
remain there. They would like to know if every number from 0 to N may still be called out
with the new drawing method considering the balls that were left in the bag.
Input
Each test case is given using exactly two lines. The first line contains two integers N and B.
The meaning of N was described above (1 ≤ N ≤ 90), while B represents the number of balls
which remained in the bag (2 ≤ B ≤ N + 1). The second line contains B distinct integers bi,
indicating the balls which remained in the bag (0 ≤ bi ≤ N).
The last test case is followed by a line containing two zeros.
Output
For each test case output a single line containing a single uppercase ‘Y’ if is possible to call out
every number from 0 to N, inclusive, or a single uppercase ‘N’ otherwise.

Albert, Charles and Mary invented a new version of the classical game Bingo. In traditional Bingo the game is presided over by a non-player known as the caller. At the beginning of the game each player is given a card containing a unique combination of numbers from 0 to N arranged in columns and rows. The caller has a bag containing N + 1 balls, numbered from 0 to N. On each turn, the caller randomly selects a ball from the bag, announces the number of the drawn ball to the players, and sets the ball aside so that it cannot be selected again. Each player searches his card for the called number and marks it if he finds it. The first player who marks a complete pre-announced pattern on the card (for example, a full horizontal line) wins a prize.

In the Albert-Charles-Mary version, on each turn, the caller draws a first ball, returns it to the bag, draws a second ball, returns it to the bag, and then calls out the absolute difference between the two ball numbers. To generate even more excitement, before the game started a possibly empty subset of balls is removed from the bag, in such a way that at least two balls remain there. They would like to know if every number from 0 to N may still be called out with the new drawing method considering the balls that were left in the bag.

Input

Each test case is given using exactly two lines. The first line contains two integers N and B. The meaning of N was described above (1 ≤ N ≤ 90), while B represents the number of balls which remained in the bag (2 ≤ B ≤ N + 1). The second line contains B distinct integers bi, indicating the balls which remained in the bag (0 ≤ bi ≤ N). The last test case is followed by a line containing two zeros.

Output

For each test case output a single line containing a single uppercase ‘Y’ if is possible to call out every number from 0 to N, inclusive, or a single uppercase ‘N’ otherwise.

Sample input

6 7
2 1 3 4 0 6 5
5 4
5 3 0 1
5 3
1 5 0
0 0

 

 

Output for the sample input

 

Y

Y

N

 

 

 


hide comments
suryadev: 2013-09-01 13:07:12

i think I/O optimization is needed

ankit kumar sinha: 2013-06-11 19:50:34

@neo can u give few test cases

Ashish: 2013-02-14 20:21:10

Finally Ac... a little Mistake cost me 4 WA... :(

karan: 2012-04-01 20:40:16

getting wa.some test cases plz..

cegprakash: 2012-04-01 16:16:36

"returns it to the bag"

Rajkiran Rajkumar: 2012-03-03 14:03:18

In the first test case, how is it possible to get 0? If we can't, then, why print 'Y' for it? Please explain :)

My bad :) Got it.

Last edit: 2012-03-03 14:04:36
saket diwakar: 2012-02-08 15:10:41

very easy:)

MR. BEAN : 2011-12-12 07:35:17

easy one :)

Jay Pandya: 2011-01-29 15:40:35

is this question is at the level of acm icpc????


Added by:~!(*(@*!@^&
Date:2010-11-04
Time limit:0.173s-1.147s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM ICPC2010 – Latin American Regional