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