Solve More Problems! CodeChef Solution

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Solve More Problems! CodeChef Solution

Solve More Problems! CodeChef Solution

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Problem

Chef came across a new online judge that has  problems, and decided that he wants to solve them.

Chef takes �� consecutive minutes to solve the -th problem, and will take a break of �� minutes immediately after solving it.
That is, Chef will solve a problem, then take a break. Solve another problem, then take another break, and so on.

Chef has  minutes of free time. If he chooses the problems and their order optimally, what is the maximum number of problems he can solve in this time?

Note that a problem is considered solved if Chef finishes solving it by the -th minute, even if the break time of the last problem extends past minute . See the sample tests below for an example.

Input Format

  • The first line of input will contain a single integer , denoting the number of test cases.
  • Each test case consists of three lines of input.
    • The first line of each test case contains two space-separated integers  and  — the number of problems in the online judge and Chef’s free time, respectively.
    • The second line of each test case contains  space-separated integers — the values �1,�2,…,��.
    • The third line of each test case contains  space-separated integers — the values �1,�2,…,��.

Output Format

For each test case, output on a new line the maximum number of problems that Chef can solve within  minutes.

Constraints

  • 1≤�≤2⋅104
  • 1≤�≤2⋅105
  • 1≤�≤108
  • 1≤��≤108
  • 0≤��≤108
  • The sum of  over all test cases won’t exceed 2⋅105.

Sample 1:

Input

Output

4
3 10
3 4 5
2 4 2
3 8
3 4 5
2 4 2
5 20
23 54 124 54 83
2 9 5 2 10
5 20
4 7 12 34 13
30 4 3 0 9
2
1
0
2

Explanation:

Test case 1: Chef can solve the first problem followed by the second problem.

  • 3 minutes for the first problem
  • 2 minutes of break time after solving it, for a total of 5 minutes
  • 5 minutes for the third problem, for a total of 10 minutes
  • There’s two minutes of break time left which goes beyond 10 minutes, but that’s ok: Chef finished solving 2 problems within 10 minutes.

Test case 2: The same times as the first sample, but with �=8. Now, Chef can solve any one problem, but cannot solve a second one no matter what.

Test case 3: Chef can’t solve anything within 20 minutes.

Test case 4: Chef can solve the third problem followed by the first problem.

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SOLUTION

Solve More Problems! CodeChef Solution

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