A very rich prince has exactly n diamonds. Each diamond 1 ≤ i ≤ n
has a certain value v_{i}. Tradition says that, before getting married,
the prince
has to give a present of value exactly V to his princess. The prince
wants to give her exactly two of his diamonds, but he does not know how to decide
*quickly* if he can do it or not. Can you help to this stupid?

For instance, if n=6 and the value of the diamonds is 5, 8, 6, 2, 6, 20, then it is possible to give a present of value V=10 (8+2) or a present of value V=12 (6+6), but it is impossible to give a present of value V=9.

Input

Input consists of several cases.
Each case begins with the gift value V
(a natural number between 1 and 10^{8})
and the number n of diamonds (a natural number between 1 and 10^{5})
in this order.
Then come n natural numbers between 1 and 10^{8}
indicating the value of each diamond.
A case with V = n = 0 marks the end of the input.

Output

For each case, print a line with “married” or “single” depending on whether the prince can give the present or not.

Public test cases

**Input**

12 6 5 8 6 2 6 20 9 6 5 8 6 2 6 20 0 0

**Output**

married single