JMU F17 Week 10

#### Start

2017-11-06 23:00 CET

## JMU F17 Week 10

#### End

2017-11-13 23:00 CET
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# Problem AThe Mailbox Manufacturers Problem

In the good old days when Swedish children were still allowed to blow up their fingers with fire-crackers, gangs of excited kids would plague certain smaller cities during Easter time, with only one thing in mind: To blow things up. Small boxes were easy to blow up, and thus mailboxes became a popular target. Now, a small mailbox manufacturer is interested in how many fire-crackers his new mailbox prototype can withstand without exploding and has hired you to help him. He will provide you with $k$ ($1 \le k \le 10$) identical mailbox prototypes each fitting up to $m$ ($1 \le m \le 100$) crackers.

However, he is not sure of how many fire-crackers he needs to provide you with in order for you to be able to solve his problem, so he asks you. You think for a while and then say:

“Well, if I blow up a mailbox I can’t use it again, so if you would provide me with only $k = 1$ mailboxes, I would have to start testing with $1$ cracker, then $2$ crackers, and so on until it finally exploded. In the worst case, that is if it does not blow up even when filled with $m$ crackers, I would need $1 + 2 + 3 + \ldots + m = \frac{m (m + 1)}{2}$ crackers. If $m = 100$ that would mean more than $5000$ fire-crackers!”

“That’s too many”, he replies. “What if I give you more than $k = 1$ mailboxes? Can you find a strategy that requires fewer fire crackers?”

Can you? And what is the minimum number of crackers that you should ask him to provide you with?

You may assume the following:

1. If a mailbox can withstand $x$ fire-crackers, it can also withstand $x-1$ fire-crackers.

2. Upon an explosion, a mailbox is either totally destroyed (blown up) or unharmed, which means that it can be reused in another test explosion.

Note: If the mailbox can withstand a full load of $m$ fire-crackers, then the manufacturer will of course be satisfied with that answer. But otherwise he is looking for the maximum number of crackers that his mailboxes can withstand.

## Input

The input starts with a single integer $N$ ($1 \le N \le 100$) indicating the number of test cases to follow. Each test case is described by a line containing two integers: $k$ and $m$, separated by a single space.

## Output

For each test case print one line with a single integer indicating the minimum number of fire-crackers that is needed, in the worst case, in order to figure out how many crackers the mailbox prototype can withstand.

Sample Input 1 Sample Output 1
4
1 10
1 100
3 73
5 100

55
5050
382
495