Description

The school track-and-field team is taking a running relay race. There are n (2<=n<=10⁴) members in the team. In order to let everybody participate in the race, each member should run at least d (0<=d<=10) meters. Besides that, everyone can run arbitrary distance. The whole length of the track is L (1<=L<=10⁵) meters.

For the i^th member in the team, if he is in a good mood , then it takes him t_i seconds (1<=t_i<=4×10⁴) to run one meter. If he is in a bad mood, then it takes him s_i (1<=s_i<=4×10⁴, 1<=t_i<=s_i) seconds to run one meter.

As the coach of the team, you can assign the running distance of each member in advance. Suppose that, it takes S seconds for the team to complete the relay race if all the members are in bad moods and it takes T seconds for the team to complete the relay race if all the members are in good moods. You do want to have a good score. But you don’t want to have a very bad score even if someone is in a bad mood. So you want to know the minimum value of T on condition that S should not be larger than W (1<=W<=2147483647).

Input

The input begins with a line containing an integer, indicating the number of test cases. There are no more than 100 test cases.

For each case, the first line begins with four integers --- the above mentioned n, d, L and W. Then n lines follow, each representing a member. Each line contains two integers s and t, meaning that the member spend s seconds to run one meter when he/she is in a bad mood, and spend t seconds to run one meter when he/she is in a good mood.

Output

For each test case, if you cannot find a proper way to assign the running distance of each member, output a string “No solution” in a line. Otherwise, output the minimum value of T (rounded to 2 digits after the decimal point) in a line.

2
2 1 20 141
8 3
6 6
3 8 20 200
8 3
6 6
7 1

88.50
No solution

Hint

In the first case, the first member runs 10.5 meters and the second member runs 9.5m. S=8×10.5+6×9.5=141=W, T=3×10.5+6×9.5=88.5.

In the second case, every member should run at least 8 meters. But the length of the track is only 20 meters. Because 8×3>20, there is no solution.

Source

Fuzhou 2011