The International Billiard Manufactory (IBM) builds the best billiard tables in the world. Its last product is the Rational Bil- liard, which is a friction-less table with volume-less balls. This means that balls just occupy a point in the space, and once they are struck with the cue, they move on the table with constant velocity, until they hit another ball. IBM wants you to build a program to analyse the behavior of balls in the Rational Billiard. The program has to decide whether a ball, struck with certain angle, will hit another ball in certain position. The figure shows the configuration of the table and the balls: m and n are integer values that indicate the size of the table. (x1, y1) and (x2, y2) are the coordinates of the first and second ball respectivelly, with 0 < x1, x2 < m and 0 < y1, y2 < n. The direction in which the first ball is struck is determined by the integer values p and q. More precisely, the slope pq determines the hitting direction of the cue, where p and q cannot be zero simultaneously. A value of p = 0 means that the ball moves parallel to the vertical axis, according to the sign of q. When the ball hits an edge, it rebounds like if the edge were a mirror (incidence angle = reflection angle). In the special case when the ball hits a corner, it is reflected on the same line but in the opposite direction of arrival. Finally, spin effects are neglected, too. Input Each line in the input corresponds to a test case specified by eight integer values: m, n, x1, y1, x2, y2, p andq,with0<m,n≤1000,0<x1,x2 <m,0<y1,y2 <n,−1000≤p,q≤1000,and|p|+|q|>0. Theendoftheinputisspecifiedbyalinewiththestring‘0 0 0 0 0 0 0 0’. Output For each test case, the program must output a line with the the text ‘HIT’ if the first ball hits the second ball, or ‘MISS’ if it does not. Sample Input 44311111 44312211 00000000 Sample Output HIT MISS