N cars are racing on a straight road. You are given their position and velocity at time t = 0. Each car is moving in the same direction with a constant positive velocity. Find the number of overtakes that take place in the race, if the race ends at time t = T₀.

A car A is said to have overtaken a car B if there exists a time t₀ such that car A was strictly behind car B for time 0 ₀ but is strictly ahead of car B for time T₀ >= t > t₀

Input

• The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
• The first line of each test case contains two space separated integers: N denoting the number of cars and T₀ denoting the race end time. In the next N lines, each contain two space separated integers: X_i and V_i, denoting the i^th car's starting position and velocity respectively.

Output

• For each test case, output a single line containing the number of overtakes that take place.

Constraints

• 1 = T = 10
• 1 = N = 10⁵
• 1 = T₀, X_i, V_i = 10⁹

Example

Input: 2 3 5 1 3 2 2 1 1 4 2 1 2 1 4 2 2 4 1 Output: 1 2

Explanation

Example case 1. The first car will overtake the second car at time 1.

Example case 2. The second car will overtake the third car at time 0.5 and the second car will overtake the fourth car at time 1. We count these towards the answer. The first car overtakes the fourth car at time 3 and the third car overtakes the fourth car at time 2. We do not count these towards the answer.