Particles
Two linear particle accelerators A and B, placed opposite to each other at a distance L apart, are propelling elementary particles. A is shooting x-particles, while B is shooting y-particles. The two kinds of particles are flying one opposing the other, and when an x-particle meets a y-particle, they collide and annihilate. One should be aware that an x particle could overtake other x-particles, as well as a y-particle could overtake other y-particles without any consequences for the particles.
Like so, in a given moment of time, which we assume to be zero, a shooting of N x-particles and N y-particles starts from the two accelerators. Each particle moves with its own constant speed. The particles are numbered in the order of their shooting from 1 to N, this holds true for both the x-particles and the y-particles.
Remark: For time t, a particle with speed v travels distance s = vt.
The shooting time moments for the x-particles are 0=tx[1] < tx[2] < tx[3] < ... < tx[N], and their speeds are vx[1], vx[2], vx[3], ..., vx[N].
Correspondingly, for the y-particles the moments are denoted by 0=ty[1] < ty[2] < ty[3] < … < ty[N], and their speeds by vy[1], vy[2], vy[3], ..., vy[N].
The shooting is executed in a way to guarantee the fulfillment of the following conditions:
Each particle will collide a particle of the opposite type;
When two particles collide, all other particles will be at a distance greater than or equal to 1 from the collision point. This is guarantee for the first К collisions.
Write a program particles to determine the first K collisions between particles of the two kinds.
####InputThe three space separated positive integers N (1 ≤ N ≤ 50000),L (1 ≤ L ≤ 10^9), and K (1 ≤ K ≤ 100) are read from the first line of the standard input.
The following N lines contain two space separated non-negative integers tx[i] (0 ≤ tx[i] ≤ 10^9) and vxi (1 ≤ vx[i] ≤ 10^9) each: the shooting moment and the speed of the corresponding x-particle.
The last N input lines contain, respectively, each the shooting moment ty[i] (0 ≤ ty[i] ≤ 10^9) and the speed vyi (1 ≤ vy[i] ≤ 10^9) of the corresponding y-particle in the same format.
####OutputThe program must print to the standard output K lines, each containing two space separated positive integers: the numbers of the x-particle and y-particle, which are involved in the corresponding collision.
Lines are output increasingly by the order of collisions – from the first one to the Kth.