# Digit Removal solution codechef

You are given an integer NN and a digit DD. Find the minimum integer you should add to NN such that the final value of NN does not contain the digit DD.

## Input Format Digit Removal solution codechef

• The first line contains TT denoting the number of test cases. Then the test cases follow.
• Each test case contains two integers NN and DD on a single line denoting the original number and the digit you need to avoid.

### Output Format Digit Removal solution codechef

For each test case, output on a single line the minimum integer you should add to NN.

• 1T1051≤T≤105
• 1N1091≤N≤109
• 0D90≤D≤9

### Subtasks Digit Removal solution codechef

• Subtask 1 (100 points): Original constraints

### Sample Input 1

5
21 5
8 8
100 0
5925 9
434356 3


### Sample Output 1  Digit Removal solution codechef

0
1
11
75
5644


## Explanation Digit Removal solution codechef

Test case 11: N=21N=21 does not contain the digit D=5D=5. Hence there is no need to add any integers to NN.

Test case 22: If 11 is added to N=8N=8, it becomes equal to 99, which does not contain the digit D=8D=8.

Test case 33: The minimum integer you should add to N=100N=100 such that the final value of NN does not contain the digit D=0D=0 is 1111.

Test case 55: The minimum integer which is greater than 434356434356 and does not contain the digit D=3D=3 is 440000440000. So we should add 440000434356=5644440000−434356=5644.

## Digit Removal solution codechef

Chef has met up with his old friend Jack recently. Jack told Chef that he found a recipe for an ancient dish, but unfortunately, it is locked in a safe and to open the safe, it is necessary to enter the solution to the following problem.

There is a sequence of non-negative integers A1,A2,,ANA1,A2,…,AN on the safe. Find the number of pairs (l,r)(l,r) (1lrN1≤l≤r≤N) which satisfy the condition

(AlAl+1Ar)(AlAl+1Ar)max(Al,Al+1,,Ar).(Al∨Al+1∨…∨Ar)⊕(Al∧Al+1∧…∧Ar)≥max(Al,Al+1,…,Ar).

Here,  denotes bitwise XOR,  denotes bitwise OR and  denotes bitwise AND.

Jack and Chef cannot think of anything except the recipe, so you are asked to open the safe.

### Input Digit Removal solution codechef

• The first line of the input contains a single integer TT denoting the number of test cases. The description of TT test cases follows.
• The first line of each test case contains a single integer NN.Digit Removal solution codechef
• The second line contains NN space-separated integers A1,A2,,ANA1,A2,…,AN.

### Output Digit Removal solution codechef

For each test case, print a single line containing one integer ― the number of pairs (l,r)(l,r) that satisfy the given condition.

### Constraints Digit Removal solution codechef

• 1N1061≤N≤106
• 0Ai<2600≤Ai<260 for each valid ii
• the sum of NN over all test cases does not exceed 106106

### Subtasks Digit Removal solution codechef

Subtask #1 (10 points): for each valid iiAiAi is a power of 22

Subtask #2 (30 points): Digit Removal solution codechef

• Ai3105Ai≤3⋅105 for each valid ii
• the sum of NN over all test cases does not exceed 31053⋅105

Subtask #3 (60 points): original constraints

### Sample Input 1  Digit Removal solution codechef

2
4
0 1 2 3
6
1 3 5 6 4 2


### Sample Output 1  Digit Removal solution codechef

6
11


### Explanation Digit Removal solution codechef

Example case 1: The pairs (l,r)(l,r) satisfying the condition are (1,1)(1,1)(1,2)(1,2)(1,3)(1,3)(1,4)(1,4)(2,3)(2,3) and (2,4)(2,4).