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Updog prepared to enjoy his delicious supper. At the very time he was ready to eat, a serious accident occurred—GtDzx appeared!! GtDzx declared his hadn't eaten anything for 3 days (obviously he was lying) and required Updog to share the cake with him. Further more, he threatened Updog that if Updog refused him, he would delete Updog's account in POJ! Thus Updog had no choice.
Updog intended to cut the cake into s (s ≥ 1) pieces evenly, and then gave t(0≤ t ≤ s) pieces to GtDzx. Apparently GtDzx might get different amount of cake for different s and t. Note that s = 12, t = 4 and s = 6, t = 2 will be regarded as the same case since GtDzx will get equal amount in the two cases. Updog wouldn't separate the cake into more than N pieces.
After sorted all available cases according to the amount of cake for GtDzx, in the first case no cake to gave to GtDzx (t = 0) and in the last case GtDzx would get the whole cake (s = t). Updog wondered that how much cake GtDzx would get in the k-th case.
The first line of the input file contains two integers N (1 ≤ N ≤ 5000) and C(0 ≤ C≤ 3000). The following C lines each contains a positive integer describe C query respectively. The i-th query ki is to ask GtDzx's share of whole cake in the ki-th case .
Answer each query in a separated line, according to the order in the input.
5 4 1 7 11 12
0/1 3/5 1/1 No Solution
POJ Monthly--2007.09.09, Updog
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