ZOJ 1003 Crashing Balloon

ZOJ Problem Set - 1003

Crashing Balloon

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Time Limit: 2 Seconds         Memory Limit: 65536 KB

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On every June 1st, the Children's Day, there will be a game named "crashing balloon" on TV.   The rule is very simple.  On the ground there are 100 labeled balloons, with the numbers 1 to 100.  After the referee shouts "Let's go!" the two players, who each starts with a score of  "1", race to crash the balloons by their feet and, at the same time, multiply their scores by the numbers written on the balloons they crash.  After a minute, the little audiences are allowed to take the remaining balloons away, and each contestant reports his\her score, the product of the numbers on the balloons he\she's crashed.  The unofficial winner is the player who announced the highest score.

Inevitably, though, disputes arise, and so the official winner is not determined until the disputes are resolved.  The player who claims the lower score is entitled to challenge his\her opponent's score.  The player with the lower score is presumed to have told the truth, because if he\she were to lie about his\her score, he\she would surely come up with a bigger better lie.  The challenge is upheld if the player with the higher score has a score that cannot be achieved with balloons not crashed by the challenging player.  So, if the challenge is successful, the player claiming the lower score wins.

So, for example, if one player claims 343 points and the other claims 49, then clearly the first player is lying; the only way to score 343 is by crashing balloons labeled 7 and 49, and the only way to score 49 is by crashing a balloon labeled 49.  Since each of two scores requires crashing the balloon labeled 49, the one claiming 343 points is presumed to be lying.

On the other hand, if one player claims 162 points and the other claims 81, it is possible for both to be telling the truth (e.g. one crashes balloons 2, 3 and 27, while the other crashes balloon 81), so the challenge would not be upheld.

By the way, if the challenger made a mistake on calculating his/her score, then the challenge would not be upheld. For example, if one player claims 10001 points and the other claims 10003, then clearly none of them are telling the truth. In this case, the challenge would not be upheld.

Unfortunately, anyone who is willing to referee a game of crashing balloon is likely to get over-excited in the hot atmosphere that he\she could not reasonably be expected to perform the intricate calculations that refereeing requires.  Hence the need for you, sober programmer, to provide a software solution.

Input

Pairs of unequal, positive numbers, with each pair on a single line, that are claimed scores from a game of crashing balloon.

Output

Numbers, one to a line, that are the winning scores, assuming that the player with the lower score always challenges the outcome.

Sample Input

343 49
3599 610
62 36

Sample Output

49
610
62

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Source: Zhejiang University Local Contest 2001
源码：



解题报告：题目的意思：分两种情况（1）高分撒谎，低分没撒谎，算低分赢。（2）其余情况算高分赢。即高分
                 低分同时撒谎；高分低分同时没撒谎；高分没撒谎，低分撒谎。
                 然后用深搜枚举出所有的公共因子的情况，（1）如果低分为一，除尽；高分不为一，没除尽，则为
                 上述第一种情况。（2）如果遇到高分低分都除尽，返回，属于第二种情况。
                  深搜枚举的时候还需注意：递归调用judge时后面n-1，这就排除了出现公共因子的情况。
                  先从大因子的开始，举例（125,25），当到因子25时，变为（5，25），此时因子跳到了24 ，继续
                  向下递归（5，25，24）这一步向下不会出现同时为一，或者到下一步（5，1，24）此时属于上述
                  第二种情况。以上说明要么25成为大数的因子，要么成为小数的因子，当大数最后不为1时，说明
                  共用了小数的因子。