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=tx1 < tx2 < tx3 < ... < txN, and their speeds are vx1, vx2, vx3, ..., vxN.

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

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.

Input

The three space separated positive integers N (1 <= N <= 50000), L (1 <= L <= 10⁹), and K (1 <= K <= 100 and K <= N) are read from the first line of the standard input.

The following N lines contain two space separated non-negative integers txi (0 <= txi <= 10⁹) and vxi (1 <= vxi <= 10⁹) each: the shooting moment and the speed of the corresponding x-particle.

The last N input lines contain, respectively, each the shooting moment tyi (0 <= tyi <= 10⁹) and the speed vyi (1 <= vyi <= 10⁹) of the corresponding y-particle in the same format.

Output

The 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.

Constraints

Time limit: 2 seconds
Memory limit: 256 megabytes

Examples

input
4 100 2
0 1
2 3
3 2
6 10
0 5
3 10
5 1
7 20

output
4 2
2 4