Contents

# For Solution

Let f(n,B)f(n,B) be the sum of digits of the integer nn when written in base BB.

Given QQ queries, each consisting of three integers n,ln,l and rr. Find the value of BB corresponding to which f(n,B)f(n,B) is minimum for all lBrl≤B≤r. If there are multiple such values, you can print any of them.

### Input Format Minimize Digit Sum solution codechef

• The first line contains in single integer QQ, the number of queries
• Each of the next Q lines contain three space separated integers n,ln,l and rr respectively.

### Output Format

• For each query (n l r), print the value of base BB which lies within [l,r][l,r] such that f(n,B)f(n,B) is minimum.

### Constraints

• 1Q1031≤Q≤103
• 2n1092≤n≤109
• 2lr1092≤l≤r≤109

### Subtasks Minimize Digit Sum solution codechef

Subtask #1 (50 points): original constraints

This problem is worth a total of 50 points and is meant to be complementary to the problem “MNDIGSM2” (also worth 50 points) which is very similar to this problem, but has slightly different constraints.

### Sample Input 1

3
216 2 7
256 2 4
31 3 5


### Sample Output 1 Minimize Digit Sum solution codechef

6
2
5


### Explanation

Test case 11: We have f(216,2)=f(216,3)=4f(216,2)=f(216,3)=4f(216,4)=6f(216,4)=6f(216,5)=8f(216,5)=8f(216,6)=1f(216,6)=1 and finally f(216,7)=12f(216,7)=12. Clearly the minimum is obtained when B=6B=6.

Test case 22: Note that f(256,2)=f(256,4)f(256,2)=f(256,4) = 22, therefore both the answers 22 and 44 will be considered correct.

Test case 33: f(31,3)=f(31,5)=3f(31,3)=f(31,5)=3 and f(31,4)=7f(31,4)=7, therefore both the answers 33 and 55 will be considered correct.