Rose is really fond of traveling and this time she decides to travel through a train. Now she is on the train. The train consists of n carriages and a strange thing about the train is that the carriages are not of the same length, the length of the ith carriage is ai meters. The distance between carriages can be neglected.

Rose noticed that the music is been played in some of the carriages. The train is approaching a railway tunnel which is h meters long. Rose does not want that at some point in time only carriages, in which there is no music, appear in the tunnel. Rose calls the moment of time silent if no music is on in all carriages, some section of the non-zero length of which is in the tunnel. To exclude the appearance of such a moment, Rose wants to play music in some carriages.

Help Rose turn on the music in the minimum number of carriages so that no moment in time is silent during the passage of the tunnel.

Input Format
The input contains several test cases. The first line contains one integer t- the number of tests. The descriptions of the tests follow.

Each test case is defined as follows: the first line contains two natural numbers n, h - the number of carriages in the train and the length of the tunnel in meters. The next line of the test contains n
natural numbers ai - the length of the carriages in meters. The next line contains n numbers, the ith
of which is equal to 1 if the music is initially on in the ith carriage, and 0 otherwise. The carriages are listed from head to tail of the train.

Note: The sum of n values for all tests does not exceed 10^6.

Output Format
For each test case, print a single number - the smallest number of carriages in which you need to turn on the music.

Constraints
1<=t<=100
1<=n<=10^5
1<=h<=10^9
1<=ai<=10^9

Example
Input
2
7 10
5 3 4 5 9 9 9
1 0 0 0 1 0 0
5 2
1 2 3 1 1
1 1 0 1 1

Output
2
1