Problem:
There are n processes in a queue. Each process has namei and timei. The round-robin scheduling handles the processes in order. A round-robin scheduler gives each process a quantum (a time slot) and interrupts the process if it is not completed by then. The process is resumed and moved to the end of the queue, then the scheduler handles the next process in the queue.

For example, we have the following queue with the quantum of 100ms.

A(150) - B(80) - C(200) - D(200)

First, process A is handled for 100ms, then the process is moved to the end of the queue with the remaining time (50ms).

B(80) - C(200) - D(200) - A(50)

Next, process B is handled for 80ms. The process is completed with the time stamp of 180ms and removed from the queue.

C(200) - D(200) - A(50)

Your task is to write a program which simulates the round-robin scheduling.

Input

n q

name1 time1

name2 time2

...

namen timen

In the first line the number of processes n and the quantum q are given separated by a single space.

In the following n lines, names and times for the n processes are given. namei and timei are separated by a single space.

Output

For each process, prints its name and the time the process finished in order.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 1000

1 ≤ timei ≤ 50000

1 ≤ length of namei ≤ 10

1 ≤ Sum of timei ≤ 1000000

Sample Input 1

5 100
p1 150
p2 80
p3 200
p4 350
p5 20

Sample Output 1

p2 180
p5 400
p1 450
p3 550
p4 800

Notes

Template in C

Solution in C (judge verdict: Accepted)

#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

struct queue_tag;
typedef struct queue_tag queue_t;
extern queue_t *queue_create(const size_t len);
extern void queue_destroy(queue_t *const q);
extern size_t queue_get_size(const queue_t *const q);
extern bool queue_enqueue(queue_t *const q, void *data, size_t len);
extern bool queue_dequeue(queue_t *const q, void *data, size_t len);

struct queue_tag {
  uint8_t *data;
  size_t size;
  size_t top;
  size_t buttom;
  size_t max_size;
};

queue_t *queue_create(const size_t len)
{
  queue_t *q = (queue_t *)malloc(sizeof(queue_t));
  if (q == NULL) goto err;

  q->data = (uint8_t *)malloc(len);
  if (q->data == NULL) goto err;

  q->size = 0;
  q->top = 0;
  q->buttom = 0;
  q->max_size = len;

  return q;

err:
  perror("memeory is full\n");
  exit(1);
}

void queue_destroy(queue_t *const q)
{
  if (q != NULL) {
    free(q->data);
  }
  free(q);

  return;
}

size_t queue_get_size(const queue_t *const q)
{
  if (q == NULL) {
    return 0;
  }

  return q->size;
}

static bool enqueue_check_params(queue_t *const q, size_t len)
{
  if (q == NULL) return false;

  if (q->max_size < len) return false;

  if (q->max_size < (q->size + len)) return false;

  return true;
}

bool queue_enqueue(queue_t *const q, void *data, size_t len)
{
  if (!enqueue_check_params(q, len)) {
    return false;
  }
  uint32_t i;
  for (i = 0; i < len; i++) {
    q->data[q->top++] = ((uint8_t *)data)[i];
    q->top %= q->max_size;
    q->size++;
  }

  return true;
}

static bool dequeue_check_params(queue_t *const q, size_t len)
{
  if (q == NULL) return false;

  if ((int32_t)((int32_t)q->size - len) < 0) return false;

  return true;
}

bool queue_dequeue(queue_t *const q, void *data, size_t len)
{
  if (!dequeue_check_params(q, len)) {
    return false;
  }
  uint32_t i;
  for (i = 0; i < len; i++) {
    ((uint8_t *)data)[i] = q->data[q->buttom++];
    q->buttom %= q->max_size;
    q->size--;
  }

  return true;
}

#if !defined(TEST)
typedef struct {
  char name[16];
  int32_t time;
} process_t;

int32_t main(void)
{
  int32_t num = 0;
  int32_t quantum = 0;
  scanf("%d %d", &num, &quantum);

  queue_t *q = queue_create(sizeof(process_t) * 256 * 1000);

  int32_t i;
  for (i = 0; i < num; i++) {
    process_t process;
    scanf("%s %d", process.name, &process.time);
    queue_enqueue(q, (void *)&process, sizeof(process));
  }

  int32_t elapsed = 0;
  while (queue_get_size(q)) {
    process_t process;
    queue_dequeue(q, (void *)&process, sizeof(process));
    if ((process.time - quantum) <= 0) {
      elapsed += process.time;
      printf("%s %d\n", process.name, elapsed);
    } else {
      process.time -= quantum;
      queue_enqueue(q, (void *)&process, sizeof(process));
      elapsed += quantum;
    }
  }
  queue_destroy(q);
  return 0;
}
#endif