
ZOJ Problem Set  2150
People are different. Some secretly read magazines full of interesting girls' pictures, others create an Abomb in their cellar, others like using Windows, and some like difficult mathematical games. Latest marketing research shows, that this market segment was so far underestimated and that there is lack of such games. This kind of game was thus included into the KOKOD��H. The rules follow: Each player chooses two numbers A_{i} and B_{i} and writes them on a slip of paper. Others cannot see the numbers. In a given moment all players show their numbers to the others. The goal is to determine the sum of all expressions A_{i}^{Bi} from all players including oneself and determine the remainder after division by a given number M. The winner is the one who first determines the correct result. According to the players' experience it is possible to increase the difficulty by choosing higher numbers. You should write a program that calculates the result and is able to find out who won the game. Input specificationThe input consists of Z assignments. The number of them is given by the single positive integer Z appearing on the first line of input. Then the assignements follow. Each assignement begins with line containing an integer M (1 <= M <= 45000). The sum will be divided by this number. Next line contains number of players H (1 <= H <= 45000). Next exactly H lines follow. On each line, there are exactly two numbers A_{i} and B_{i} separated by space. Both numbers cannot be equal zero at the same time. Output specificationFor each assingnement there is the only one line of output. On this line, there is a number, the result of expression(A_{1}^{B1} + A_{2}^{B2} + ... + A_{H}^{BH}) mod M. Sample Input3 16 4 2 3 3 4 4 5 5 6 36123 1 2374859 3029382 17 1 3 18132 Output for the Sample Input2 13195 13
Source: Czech Technical University Open 1999 