CF1763B Incinerate

To 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 $ ^\dagger $ weakest monster $ ^\ddagger $ alive. In other words, the minimum $ p_i $ among all currently living monsters is subtracted from the value of $ k $ after each attack. $ ^\dagger $ The Weakest monster is the one with the least power. $ ^\ddagger $ A monster is alive if its health is strictly greater than $ 0 $ . Will Genos be successful in killing all the monsters?

The 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 $ .

For each test case, print the answer — "YES" (without quotes) if Genos could kill all monsters and "NO" otherwise.

In 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.