Cross Country Race

The organizers of the interval start cross country world championship made a serious mistake. Nowhere on the course can a runner pass the person in front. If a runner catches the person who started before them, the two have to stay together for the rest of the race.

That is no way to decide a world champion, so the organizers record only the times of the runners who cross the finish line with nobody right in front of them. The others rest and then run another race, and that race decides their times.

The risk in this setup is that far too many races may be needed. Given the length of the course and the speeds of the participants, find how many races have to be arranged.

Within one race the runners start one minute apart, in the order given in the input. In a later race the relative order of the runners is the same, and only their start times are adjusted, so the gap between two consecutive starts is still exactly one minute.

The first line contains the number of test cases $T$. Each test case begins with a line holding the number of participants $N$ and the length of the course $S$ in meters. The next line holds the speeds $v_1, v_2, \dots, v_N$ of the participants in start order, in meters per minute.

• $0 < T \le 100$
• $0 < N \le 1000$
• $0 < S \le 50000$
• $0 < v_i < 1000$
• Every number in the input is an integer.
• Each participant counts as a single point.
• A participant can reach the exact point where an earlier starter is, but cannot pass that point.
• A participant has someone right in front of them exactly when the two are at the same point and that participant is not the one who started first of the two.
• The distance $s$, the speed $v$ and the time $t$ satisfy $s = v \times t$.

For each test case, print the number of races that have to be arranged, one per line.