Problem Statement

A train goes back and forth between Town $A$ and Town $B$. It departs Town $A$ at time $0$ and then repeats the following:

• goes to Town $B$, taking $X$ seconds;
• stops at Town $B$ for $Y$ seconds;
• goes to Town $A$, taking $X$ seconds;
• stops at Town $A$ for $Y$ seconds.

More formally, these intervals of time are half-open, that is, for each $n = 0, 1, 2, \dots$:

• at time $t$ such that $(2X + 2Y)n ≤ t < (2X + 2Y)n + X$, the train is going to Town $B$;
• at time $t$ such that $(2X + 2Y)n + X ≤ t < (2X + 2Y)n + X + Y$, the train is stopping at Town $B$;
• at time $t$ such that $(2X + 2Y)n + X + Y ≤ t < (2X + 2Y)n + 2X + Y$, the train is going to Town $A$;
• at time $t$ such that $(2X + 2Y)n + 2X + Y ≤ t < (2X + 2Y)(n + 1)$, the train is stopping at Town $A$.

Takahashi is thinking of taking this train to depart Town $A$ at time $0$ and getting off at Town $B$. After the departure, he will repeat the following:

• be asleep for $P$ seconds;
• be awake for $Q$ seconds.

Again, these intervals of time are half-open, that is, for each $n = 0, 1, 2, \dots$:

• at time $t$ such that $(P + Q)n ≤ t < (P + Q)n + P$, Takahashi is asleep;
• at time $t$ such that $(P + Q)n + P ≤ t < (P + Q)(n + 1)$, Takahashi is awake.

He can get off the train at Town $B$ if it is stopping at Town $B$ and he is awake. Determine whether he can get off at Town $B$. If he can, find the earliest possible time to do so. Under the constraints of this problem, it can be proved that the earliest time is an integer.

You are given $T$ cases. Solve each of them.

Constraints

• All values in input are integers.
• $1 ≤ T ≤ 10$
• $1 ≤ X ≤ 10^9$
• $1 ≤ Y ≤ 500$
• $1 ≤ P ≤ 10^9$
• $1 ≤ Q ≤ 500$

Input

Input is given from Standard Input in the following format:

T
\rm case_1
\rm case_2
\hspace{9pt}\vdots
\rm case_T

Each case is in the following format:

X Y P Q

Output

Print $T$ lines. The $i$-th line should contain the answer to $\rm case_i$. If there exists a time such that Takahashi can get off the train at Town $B$, the line should contain the earliest such time; otherwise, the line should contain infinity.