B. Incineratetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputTo destroy humanity, The Monster Association sent n monsters to Earth's surface. The i-th monster has health h_i and power p_i.With his last resort attack, True Spiral Incineration Cannon, Genos can deal k damage to all monsters alive. In other words, Genos can reduce the health of all monsters by k (if k > 0) with a single attack. However, after every attack Genos makes, the monsters advance. With their combined efforts, they reduce Genos' attack damage by the power of the ^\daggerweakest monster ^\ddaggeralive. In other words, the minimum p_i among all currently living monsters is subtracted from the value of k after each attack.^\daggerThe Weakest monster is the one with the least power.^\ddaggerA monster is alive if its health is strictly greater than 0.Will Genos be successful in killing all the monsters?InputThe first line of the input contains a single integer t (1 \le t \le 100) — the number of test cases. The description of test cases follows.The first line of each test case contains two integers, n and k (1 \le n, k \le 10^5) — the number of monsters and Genos' initial attack damage. Then two lines follow, each containing n integers describing the arrays h and p (1 \le h_i, p_i \le 10^9).It's guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, print the answer — "YES" (without quotes) if Genos could kill all monsters and "NO" otherwise.ExampleInput
36 718 5 13 9 10 12 7 2 1 2 63 45 5 54 4 43 22 1 31 1 1Output
YES
NO
YES
NoteIn the first example, after Genos' first attack, h and k will update to:   h: [11,0,6,2,3,0]  k: 7-1 = 6  After second attack:   h: [5,0,0,0,0,0]  k: 6-2 = 4  After third attack:   h: [1,0,0,0,0,0]  k: 4-2 = 2  After fourth attack:   h: [0,0,0,0,0,0]  As Genos could kill all monsters, the answer is YES.
36 718 5 13 9 10 12 7 2 1 2 63 45 5 54 4 43 22 1 31 1 1
YES NO YES 
['binary search', 'brute force', 'data structures', 'implementation', 'math', 'sortings', '*1200']