Fried-chicken is a devoted player of Hearthstone. Since the game resumed operations in the Chinese mainland, he has been obsessed with it and reached Silver 2 rank in Standard mode. Today, while ranking up using Death Knight, he encountered a formidable opponent, Stewed-chicken, and was left with just $$$1$$$ Health. To survive, Fried-chicken must eliminate all of Stewed-chicken's minions. Fortunately, he can use spell cards and his minions' attacks to achieve this goal.
Specifically, this game involves two factions: Fried-chicken and Stewed-chicken. Each faction has some minions. The $$$i$$$-th minion has $$$h_i$$$ Health. It is now Fried-chicken's turn, and each of his minions can attack any one minion from the opposing faction at most once. When one minion attacks another, both minions lose $$$1$$$ Health. If a minion's Health is reduced to $$$0$$$ or less, it dies and can no longer attack or be attacked.
To achieve his goal, Fried-chicken casts the spell "Threads of Despair," causing every minion to explode upon death, which reduces the Health of all minions by $$$1$$$. If the explosion causes the death of other minions, other minions will also explode immediately. Fried-chicken cannot have his minions attack other minions until all explosion effects have finished. After casting the spell, Fried-chicken can make his minions attack Stewed-chicken's minions in any order he chooses. He wants to know if there exists an attack order that allows Fried-chicken to eliminate all of Stewed-chicken's minions.
Each test file contains multiple test cases. The first line contains the number of test cases $$$T$$$ ($$$1 \leq T \leq 5 \times 10^5$$$). The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 5 \times 10^5$$$), representing the number of Fried-chicken's minions and Stewed-chicken's minions, respectively.
The second line contains $$$n$$$ integers $$$h_1, h_2, \dots, h_n$$$ ($$$1 \leq h_i \leq 10^9$$$), where $$$h_i$$$ represents the Health of Fried-chicken's $$$i$$$-th minion.
The third line contains $$$m$$$ integers $$$h'_1, h'_2, \dots, h'_m$$$ ($$$1 \leq h'_i \leq 10^9$$$), where $$$h'_i$$$ represents the Health of Stewed-chicken's $$$i$$$-th minion.
For each test file, it is guaranteed that the sum of all $$$n$$$ across all test cases does not exceed $$$5 \times 10^5$$$, and the sum of all $$$m$$$ across all test cases does not exceed $$$5 \times 10^5$$$.
For each test case, output "Yes" if Fried-chicken can eliminate all of Stewed-chicken's minions; otherwise, output "No".
You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.
33 21 1 42 63 21 1 42 72 1100 1002
Yes No Yes
37 11 1 1 1 1 1 195 23 4 5 6 71 65 33 4 5 6 71 5 7
No No Yes
In the first test case of Sample 1, one possible sequence of actions is as follows: Fried-chicken's $$$3$$$rd minion attacks Stewed-chicken's $$$2$$$nd minion, followed by Fried-chicken's $$$2$$$nd minion attacking Stewed-chicken's $$$2$$$nd minion. At this point, Fried-chicken's $$$2$$$nd minion dies, triggering an explosion. This explosion causes further deaths, leading to a chain reaction of explosions. Eventually, all minions are eliminated.
In the third test case of Sample 1, one possible sequence of actions is as follows: Fried-chicken's $$$1$$$st minion attacks Stewed-chicken's $$$1$$$st minion, followed by Fried-chicken's $$$2$$$nd minion attacking Stewed-chicken's $$$1$$$st minion. At this point, Stewed-chicken's $$$1$$$st minion dies, triggering an explosion. Ultimately, Fried-chicken is left with two minions, each having $$$98$$$ Health, while all of Stewed-chicken's minions are eliminated. Fried-chicken survives successfully.
