SPOJ.com - Problem LASTDIG

LASTDIG - The last digit

#number-theory #ad-hoc-1

Nestor was doing the work of his math class about three days but he is tired of make operations a lot and he should deliver his task tomorrow. His math’s teacher gives him two numbers a and b. The problem consist of finding the last digit of the potency of base a and index b. Help Nestor with his problem. You are given two integer numbers: the base a (0 <= a <= 20) and the index b (0 <= b <= 2,147,483,000), a and b both are not 0. You have to find the last digit of a^b.

Input

The first line of input contains an integer t, the number of test cases (t <= 30). t test cases follow. For each test case will appear a and b separated by space.

Output

For each test case output an integer per line representing the result.

Example

Input:
2
3 10
6 2

Output:
9
6

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	g4mewarrior: 2016-01-15 16:18:59 diff outputs in diff line costed me a wa simple prob of modular exponentiation take modulus at each step for base and output can be done with int only
	code_nit: 2015-12-25 08:27:31 Awesome problem !! AC !! :)
	Timmy Jose: 2015-11-24 19:58:42 Life lesson, guys - always generate your own test cases to test against before submitting!
	Timmy Jose: 2015-11-24 19:42:25 Infernal problem! Thanks to the guy who suggested testing from 0 0 till 10 5. That helped me fix my edge cases. Damn!
	garmel: 2015-10-17 02:34:17 hhh...If you have the problem of 700MB....you have to look for a solution near to yours... In fact, you can remarque that all the cases a%10(9cases) can be resumed into just one....mod 4 is the solution... just you have to take cases b==0 and a==0, each one alone, then b%=4; after that If b==0, you must put b=4 because when you look at case a%10==8, 8^0 is different from 8^4 Then you make b=pow(a, b)%10 and finally cout<<b<<'\n'; Last edit: 2015-10-17 02:34:59
	satish: 2015-10-11 10:13:41 what's the idea @ Vivek
	kubas: 2015-10-07 20:16:25 "a and b both are not 0" This means that when a == 0 then b != 0; when b==0 then a != 0. A test case where a==0 and b==0 is excluded.
	anshulwarade: 2015-09-29 15:37:34 Really easy sum....but it is saying wrong answer in this....but on my pc's compiler its working good...what is the reason?
	Vivek: 2015-09-22 23:24:22 Really easy.. You don't even Need to remember pattern of various digits such as for 3->3,9,7,1 and so on. was pending for 6 months.. 1 night simple idea, got AC in two mins. Last edit: 2015-09-22 23:28:40
	shshnk28: 2015-09-12 17:12:22 every number repeats after a certain number times

Submit solution!

Added by:	Jose Daniel Rodriguez Morales
Date:	2008-12-01
Time limit:	1s
Source limit:	700B
Memory limit:	1536MB
Cluster:	Cube (Intel G860)
Languages:	All except: GOSU
Resource:	Own