408817: GYM103329 B Might and Magic

Two heroes are fighting, whose names are hero $$$0$$$ and hero $$$1$$$ respectively.

You are controlling the hero $$$0$$$, and your enemy is the hero $$$1$$$. Each hero has five integer attributes: ATTACK, DEFENSE, POWER, KNOWLEDGE, and HEALTH. When two heroes battle with each other, they will take turns to attack, and your hero moves first. One hero can make $$$\textbf{exactly one attack}$$$ in one turn, either a physical attack or a magical attack.

Assume their attributes are $$$A_i$$$, $$$D_i$$$, $$$P_i$$$, $$$K_i$$$, $$$H_i$$$ ($$$0 \leq i \leq 1)$$$. For hero $$$i$$$, its physical attack's damage is $$$C_p \cdot \max (1, A_i - D_{1-i})$$$, while its magical attack's damage is $$$C_m \cdot P_i$$$. Here, $$$C_p$$$ and $$$C_m$$$ are given constants.

After hero $$$i$$$'s attack, $$$H_{1-i}$$$ will decrease by the damage of its enemy. If $$$H_{1-i}$$$ is lower or equal to $$$0$$$, the hero $$$(1-i)$$$ loses, the hero $$$i$$$ wins, and the battle ends.

Hero $$$i$$$ can make magical attacks no more than $$$K_i$$$ times in the whole battle.

Now you know your enemy is a Yog who is utterly ignorant of magic, which means $$$P_1 = K_1 = 0$$$, and he will only make physical attacks. You can distribute $$$N$$$ attribute points into four attributes $$$A_0$$$, $$$D_0$$$, $$$P_0$$$, $$$K_0$$$ arbitrarily, which means these attributes can be any non-negative integers satisfying $$$0 \leq A_0 + D_0 + P_0 + K_0 \leq N$$$.

Given $$$C_p$$$, $$$C_m$$$, $$$H_0$$$, $$$A_1$$$, $$$D_1$$$, and $$$N$$$, please calculate the maximum $$$H_1$$$ such that you can build hero $$$0$$$ and fight so that it wins the game.

The first line contains an integer $$$T$$$ ($$$1 \leq T \leq 10^4$$$), the number of test cases. Then $$$T$$$ test cases follow.

The first and only line of each test case contains six integers $$$C_p$$$, $$$C_m$$$, $$$H_0$$$, $$$A_1$$$, $$$D_1$$$, $$$N$$$ ($$$1 \leq C_p, C_m, H_0, A_1, D_1, N \leq 10^6$$$), the attributes described above.

For each test case, print a line with one integer: the maximum enemy health such that it is possible to win.

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1 1 4 5 1 4
2 5 1 9 9 6

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