UVa 11889 Benefit (number theory)

11889-benefit

Time limit:5.000 seconds

Http://uva.onlinejudge.org/index.php? OPTION=COM_ONLINEJUDGE&ITEMID=8&CATEGORY=467&PAGE=SHOW_PROBLEM&PROBLEM=29 89

Recently Yaghoub is playing a new trick to sell some. When somebody gives him A Tomans, Him who never has the appropriate, changes for B asks Tomans St Common multiple of a and B equals to C and he'll pay back A round bill. Or otherwise take some snack instead of the remaining of his. He believes that finding such a number are hard enough that dissuades students from paying that.

You are should write a program this help poor students giving the appropriate amount of. Of course if there are several answers your go for students ' benefit which is the lowest of them.

Input

The number of tests is the number of the 100000. Each test is comes in a separate line contains two integers a and C (1a, c ⁷).

Output

Print the lowest integer B such that LCM(a, B) = C in A single line . If No such integer exists, print "no SOLUTION" instead. (Quotes for clarity)

Sample Input

3
2 6
1760
7 16

Sample Output

3
NO SOLUTION

Ideas:

We can use a and C's unique factor decomposition to find the smallest possible B-factor factorization, and then find B, but the complexity of this method is O (c).

Is there a quicker way?

Method 2:

Because

AB/GCD (a,b) =c,

Remember c/a as B ', then

B=b ' gcd (a,b),

Set

B=kb ',

Then there are

GCD (A,KB ') =k,