Yeongwoo and God4

Yeongwoo is playing a game called God4 again. In God4 every character and every monster has an attack $A$, a defence $D$, and a maximum health $H$. Combat is always one on one and runs by these rules.

1. On your turn you attack the other side. The defender loses the larger of (attacker's attack $-$ defender's defence) and $1$ health.
2. When the attack ends, the turn passes to the other side.
3. The two sides keep taking turns until one side's health drops to $0$ or below. The side whose health drops first loses.
4. Yeongwoo's character always attacks first.

When the character wins, it absorbs the monster's stats exactly as they are. A character with stats $(5, 5, 5)$ that beats a monster with stats $(1, 1, 1)$ ends up with $(6, 6, 6)$. Every win also restores the character's health to its maximum, so every fight starts at full health.

Yeongwoo wants to beat $N$ monsters in a row without a single loss, which means he has to win every fight. Listing the data of all $N$ monsters would make the input far too large, so the stats of the $k$-th monster for $k > 1$ come from these formulas.

$A_k = ((A_{k-1} \times A_p + A_a) \bmod 100) + 1$

$D_k = ((D_{k-1} \times D_p + D_a) \bmod 3) + 1$

$H_k = ((H_{k-1} \times H_p + H_a) \bmod 1000) + 1$

The program reads from standard input.

The first line contains the number of monsters $N$. ($1 \le N \le 5 \times 10^7$)

The second line contains the attack $A$, the defence $D$, and the maximum health $H$ of Yeongwoo's character, in that order. ($1 \le A \le 100$, $1 \le D \le 3$, $1 \le H \le 1000$)

The third line contains the attack $A_1$, the defence $D_1$, and the maximum health $H_1$ of the first monster, in that order. ($1 \le A_1 \le 100$, $1 \le D_1 \le 3$, $1 \le H_1 \le 1000$)

The fourth line contains the values $A_p$, $A_a$, $D_p$, $D_a$, $H_p$, $H_a$ used to generate the monster stats, in that order. ($1 \le A_p, D_p, H_p \le 10^9$, $0 \le A_a \le 99$, $0 \le D_a \le 2$, $0 \le H_a \le 999$)

The program writes to standard output.

If Yeongwoo beats all $N$ monsters, print the character's final stats on one line in the order attack, defence, maximum health, separated by single spaces. Print each of the three values modulo $10^9 + 7$.

If he loses even once, print -1 on the first line and nothing else.