CF1760F.Quests

There are $n$ quests. If you complete the $i$ -th quest, you will gain $a_i$ coins. You can only complete at most one quest per day. However, once you complete a quest, you cannot do the same quest again for $k$ days. (For example, if $k=2$ and you do quest $1$ on day $1$ , then you cannot do it on day $2$ or $3$ , but you can do it again on day $4$ .)

You are given two integers $c$ and $d$ . Find the maximum value of $k$ such that you can gain at least $c$ coins over $d$ days. If no such $k$ exists, output Impossible. If $k$ can be arbitrarily large, output Infinity.

The input consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains three integers $n,c,d$ ( $2 \leq n \leq 2\cdot10^5$ ; $1 \leq c \leq 10^{16}$ ; $1 \leq d \leq 2\cdot10^5$ ) — the number of quests, the number of coins you need, and the number of days.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \leq a_i \leq 10^9$ ) — the rewards for the quests.

The sum of $n$ over all test cases does not exceed $2\cdot10^5$ , and the sum of $d$ over all test cases does not exceed $2\cdot10^5$ .

For each test case, output one of the following.

• If no such $k$ exists, output Impossible.
• If $k$ can be arbitrarily large, output Infinity.
• Otherwise, output a single integer — the maximum value of $k$ such that you can gain at least $c$ coins over $d$ days.

Please note, the checker is case-sensitive, and you should output strings exactly as they are given.

In the first test case, one way to earn $5$ coins over $4$ days with $k=2$ is as follows:

• Day 1: do quest 2, and earn $2$ coins.
• Day 2: do quest 1, and earn $1$ coin.
• Day 3: do nothing.
• Day 4: do quest 2, and earn $2$ coins.

In total, we earned $2+1+2=5$ coins.In the second test case, we can make over $20$ coins on the first day itself by doing the first quest to earn $100$ coins, so the value of $k$ can be arbitrarily large, since we never need to do another quest.

In the third test case, no matter what we do, we can't earn $100$ coins over $3$ days.