SNGLOOP1 - Easiest Loop 1

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Ileana D'Cruz is taking programming classes but she is having problem in understanding while loops. She is working on following set of instructions -

INTEGER I = 0, S, U = 1010;

WHILE (I < U) {
S = (3 * S) + (5 * I);
I = I + 1;
}

Let Sk be the value assigned to INTEGER S for the iteration I = (k + 1) and n, m, p be positive integers such that m > n. Ileana knows the values of n and m but she forgot the initial value of S. She is trying to find the unit digit of p. Any initial value of S may be used. She also knows the following equality -

(2 * n + 3) * (p - 1) + (4 / 5) * [(p * Sn) - Sm] = 2 * (m - n)

Input

First line of input is T(total no. of test cases). Each of next T lines contains two integers n and m.

Output

Print unit digit of p (p % 10) for each test case in separated lines.

Example

Input:
1
2 3

Output:
3

Constraints

T < 10001

Explanation

Let S = 2
S0 = 6
S1 = 23
S2 = 79
S3 = 252
Now solving the equation gives p = 3.


hide comments
prabhav_123: 2019-01-08 19:02:36

getting back to the very basic concept of physics's derivations, finally got me an AC! Pheww

Last edit: 2019-01-08 19:26:38
mcjoshi: 2016-02-27 13:25:54

took my 3 hours! AC
@ping_of_death: :...खोदा पहाड़ निकली चुहिया...: agree_with_U

KD : 2016-01-01 19:17:13

Damn easy
but it makes my century :)

Last edit: 2016-01-01 19:17:35
Siddharth Singh: 2015-12-26 12:49:34

Interesting One , the given explanation Helped me device a trial an error formula which to my surprise worked :D
AC in 1 go <3

vagesh_verma: 2015-08-16 10:05:04

Last edit: 2015-08-16 10:06:32
मोहन: 2015-02-06 11:51:34

Here comes a my 100th!!! :)

Saksham : 2015-01-09 13:19:16

a very good indeed

bourne: 2014-12-15 10:15:38

I think @Rahul Jain is correct. Not satisfying for S=0. Although the proof is easy for other values of S. Ignore the pattern and Try it :) !

Vamsi Krishna Avula: 2014-12-15 07:28:22

I was not able to prove it mathematically but observing the pattern was easy enough.

NEXES: 2014-11-29 18:42:26

AC in one go.....
solve it and the see the beauty of mathematics


Added by:AvmnuSng
Date:2014-06-14
Time limit:0.119s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:Abhimanyu Singh
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