Train in a Tunnel

Peter is traveling by train. The train has $n$ cars, and the $i$-th car is $a_i$ meters long. Assume there is no gap between cars.

Some of the cars have their light on and the rest have it off. The train is about to enter a tunnel of length $h$ meters. A moment is dark if every car that has a part of nonzero length inside the tunnel has its light off. A car that touches the tunnel entrance or exit at a single point only does not count as being inside the tunnel.

Peter wants no dark moment from the instant the front of the train enters the tunnel until the instant the rear of the train leaves it. The lights that are already on stay on. Find the smallest number of cars whose light Peter has to turn on.

The first line contains the number of test cases $t$ ($1 \le t \le 100$).

The first line of each test case contains the number of cars $n$ and the length of the tunnel $h$ ($1 \le n \le 10^5$, $1 \le h \le 10^9$). The second line contains the car lengths $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$). The third line contains $n$ integers, where the $i$-th value is $1$ if the light of the $i$-th car is on and $0$ if it is off. The cars are given in the order they enter the tunnel.

The sum of $n$ over all test cases does not exceed $10^6$.

For each test case, print on one line the smallest number of cars whose light must be turned on so that no dark moment occurs.