B"There are n cities in Byteland, some of which are connected by roads, which can be traversed in any direction. The i -th road has its own hardness parameter w_i . Time spent on traversing a road with its hardness equal to w_i is lceil frac{w_i}{c} rceil , where c is the current driving skill. The travel network of Byteland is a tree. In other words, between any pair of cities, there is exactly one path that passes through each city at most once. In some cities you can visit driving courses. A single course takes T time to complete, and after completing the course the driver's skill c is increased by 2 times. Notice that the time T required to complete a course is the same in all cities, and courses can be completed in the same city more than once. You need to answer the q queries: what is the minimum time it takes to get from the city a to city b if you start the travelling with driving skill c = 1 ? Each test contains multiple test cases. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The description of the test cases follows. The first line of each test case contains two integers n and T ( 1 <= n <= 10^5, 1 <= T <= 10^6 ) - the number of cities and time required to complete a single driving course. The following n - 1 lines each contain three integers u_i , v_i and w_i ( 1 <= u_i, v_i <= n, 1 <= w_i <= 10^6, u_i neq v_i ), which mean that there exists a road connecting towns u_i and v_i with hardness equal to w_i . The next line contains a binary string s of length n , consisting only of symbols 0 and 1 . If s_i = 1 ( 1 <= i <= n ), then you can visit driving courses in the i -th city. If s_i = 0 ( 1 <= i <= n ), then you cannot visit driving courses in the i -th city. The next line contains a s"...