Road

A country has N cities numbered 1 through N. An engineer wants to build roads so that every city can reach every other city, passing through other cities on the way if needed.

His team surveyed M routes that could carry a road. Each route joins two cities in both directions, and paving a road along a route costs a fixed amount. The shorter the route, the cheaper it is.

The engineer did not plan the transport system in advance. He just picks a route he likes, paves a road on it, and repeats until every city is connected.

Right now he wants to pave the route between city p and city q. The government is pressing him to cut costs, so he asked you for a program that decides whether he may build that road. Print YES if a road network of the smallest possible total cost that connects every city can contain that road, and NO otherwise.

The first line contains the number of test cases T. ($T \le 10$)

The first line of each test case contains the integers N, M, p, q. N ($2 \le N \le 10\,000$) is the number of cities, M ($1 \le M \le 20\,000$) is the number of routes, and p and q ($1 \le p, q \le N$) are the two cities in question.

Each of the next M lines contains the integers u, v, w. ($1 \le u \le N$, $1 \le v \le N$, $1 \le w \le 400\,000$) The route joining city u and city v in both directions costs w.

Within one test case all route costs are different, and at most one route joins any pair of cities. The route between p and q is one of the M given routes. At least one road network connecting every city is guaranteed to exist. Every input value is an integer.

Print one line per test case. Print YES if a road network of the smallest possible total cost can contain the road between p and q, and NO otherwise.