15797번 - Particles 다국어

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 xparticle 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=tx₁ < tx₂ < tx₃ < …. < tx_N, and their speeds are vx₁, vx₂, vx₃, ..., vx_N.

Correspondingly, for the y-particles the moments are denoted by 0=ty₁ < ty₂ < ty₃ < … < ty_N, and their speeds by vy₁, vy₂, vy₃, ..., 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.

The three space separated positive integers N, L, and K are read from the first line of the standard input.

The following N lines contain two space separated non-negative integers tx_i and vx_i 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 and the speed vy_i of the corresponding y-particle in the same format.

The program must print to the standard output K lines, each containing two space separated positive integers: the numbers of the xparticle 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.

• 1 ≤ N ≤ 50 000
• In 30% of the tests N ≤ 1000
• 1 ≤ L ≤ 10⁹
• 1 ≤ K ≤ 100, K ≤ N
• 0 ≤ tx_i, ty_i ≤ 10⁹
• 1 ≤ vx_i, vy_i ≤ 10⁹