C. Kill the Monstertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputMonocarp is playing a computer game. In this game, his character fights different monsters.A fight between a character and a monster goes as follows. Suppose the character initially has health h_C and attack d_C; the monster initially has health h_M and attack d_M. The fight consists of several steps:  the character attacks the monster, decreasing the monster's health by d_C;  the monster attacks the character, decreasing the character's health by d_M;  the character attacks the monster, decreasing the monster's health by d_C;  the monster attacks the character, decreasing the character's health by d_M;  and so on, until the end of the fight. The fight ends when someone's health becomes non-positive (i. e. 0 or less). If the monster's health becomes non-positive, the character wins, otherwise the monster wins.Monocarp's character currently has health equal to h_C and attack equal to d_C. He wants to slay a monster with health equal to h_M and attack equal to d_M. Before the fight, Monocarp can spend up to k coins to upgrade his character's weapon and/or armor; each upgrade costs exactly one coin, each weapon upgrade increases the character's attack by w, and each armor upgrade increases the character's health by a.Can Monocarp's character slay the monster if Monocarp spends coins on upgrades optimally?InputThe first line contains one integer t (1 \le t \le 5 \cdot 10^4) — the number of test cases. Each test case consists of three lines:The first line contains two integers h_C and d_C (1 \le h_C \le 10^{15}; 1 \le d_C \le 10^9) — the character's health and attack;The second line contains two integers h_M and d_M (1 \le h_M \le 10^{15}; 1 \le d_M \le 10^9) — the monster's health and attack;The third line contains three integers k, w and a (0 \le k \le 2 \cdot 10^5; 0 \le w \le 10^4; 0 \le a \le 10^{10}) — the maximum number of coins that Monocarp can spend, the amount added to the character's attack with each weapon upgrade, and the amount added to the character's health with each armor upgrade, respectively.The sum of k over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, print YES if it is possible to slay the monster by optimally choosing the upgrades. Otherwise, print NO.ExampleInput
4
25 4
9 20
1 1 10
25 4
12 20
1 1 10
100 1
45 2
0 4 10
9 2
69 2
4 2 7
Output
YES
NO
YES
YES
NoteIn the first example, Monocarp can spend one coin to upgrade weapon (damage will be equal to 5), then health during battle will change as follows: (h_C, h_M) = (25, 9) \rightarrow (25, 4) \rightarrow (5, 4) \rightarrow (5, -1). The battle ended with Monocarp's victory.In the second example, Monocarp has no way to defeat the monster.In the third example, Monocarp has no coins, so he can't buy upgrades. However, the initial characteristics are enough for Monocarp to win.In the fourth example, Monocarp has 4 coins. To defeat the monster, he has to spend 2 coins to upgrade weapon and 2 coins to upgrade armor.
4
25 4
9 20
1 1 10
25 4
12 20
1 1 10
100 1
45 2
0 4 10
9 2
69 2
4 2 7

YES NO YES YES 
['brute force', 'math', '*1100']