LASTDIG - The last digit


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 ab.

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

hide comments
captaindavinci: 2017-11-18 12:57:07

In this problem you could solve it by calculating (a ^ b) % 10, using fast modular exponentiation. Time complexity would be O(logb)

sinersnvrsleep: 2017-11-06 20:24:59

there occurs a pattern in the power of digits one needs to find that and its done

sandilya1599: 2017-09-27 08:12:53

python is love

mahilewets: 2017-08-28 20:16:47

Very funny

LSTDGT which is much bigger a and much bigger b

Is just tutorial now

But this problem is classic

mahilewets: 2017-08-28 20:12:55

Python does the job

softxide: 2017-08-10 13:33:02

you can easily do the solution in O(4) space and O(4) time if you keep track of pattern in last digit .
Furthermore problem says a and b cant be zero , but there are test cases as per range if a and b .

larunrahul: 2017-07-04 18:21:58

Hint: The pattern repeats for every 4 powers of last digit of 'a'. Such a simple but tricky one. Observe the pattern.

manish_nit97: 2017-06-30 21:03:50

power function will not work here. a^b can't be dealt with primitive data types. Use mathematical properties and that's it!!

heybob: 2017-06-28 20:55:48

Can someone explain the procedure to solve it without pow(). THanks

coder_at_work: 2017-06-26 07:56:13

Your source code shouldn't occupy more than 700 bytes, so remove unnecessary header files, whitespace etc. Easy problem, try to observe pattern. No need of using pow() function.


Added by:Jose Daniel Rodriguez Morales
Date:2008-12-01
Time limit:0.340s
Source limit:700B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: GOSU
Resource:Own