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Magician's Offer!

By Ariful_Efath · Limits 2s, 512 MB

Rosi Vidmun is a greedy landlord who likes to grab as much land as he can. Currently he has PP square km land and he wants more! Nobody likes Rosi, but he doesn’t bother about it. Yesterday, a Magician came to him and gave him an offer of giving a larger land. He will get a land of PXP^X square km, but only if he is able to solve a puzzle. Magician has a land having Infinite length and width. Rosi is free to select any length and width from the top left corner of the land. He needs to answer how many possible ways are there to make PXP^X square km land where the length and width must be a positive integer. If he takes the offer and fails to answer, the magician will take all of his land. Rosi was confused to take the offer. So, the magician told him, he will count the answer as correct if Rosi could tell the last 7 digits of the actual answer. As 7 is a lucky number, Rosi took the offer and thought that it will bring luck to him. I know you might also have started hating Rosi! But, help him to find the answer he needs. He might give you 10% of the land!

Rosi is assuming that the magician might change the value of PP and XX before asking him the answer. So, you have to solve it for different values of PP and XX.


Input starts with a positive integer TT (1000≤ 1000) denoting the number of test cases.

Each case starts with a line containing two integers PP and XX where 1P10121 ≤ P ≤ 10^{12} and 1X1051 ≤ X ≤ 10^5.


Output should consist of exactly TT lines, one for each test case. Each line should be of the format "Case X: Y" (without the quotes), where XX is the test case and YY is the last 7 digits of the answer that Rosi needs. If the answer has less than 7 digits, print it with leading zeros.


6 1
7 2
30 300
Case 1: 0000004
Case 2: 0000003
Case 3: 7270901

For P=6P=6 and X=1X=1, Rosi has the following ways to select his land.



82% Solution Ratio

forthright48Earliest, Feb '16

tuhin107494Fastest, 0.2s

kfoozminusLightest, 1.3 MB

steinumShortest, 729B


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