Problem: All modern mobile applications are divided into free and paid. Even a single application developers often release two versions: a paid version without ads and a free version with ads.

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Suppose that a paid version of the app costs p (p is an integer) rubles, and the free version of the application contains c ad banners. Each user can be described by two integers: ai — the number of rubles this user is willing to pay for the paid version of the application, and bi — the number of banners he is willing to tolerate in the free version.

The behavior of each member shall be considered strictly deterministic:

  * if for user i, value bi is at least c, then he uses the free version, 
  * otherwise, if value ai is at least p, then he buys the paid version without advertising, 
  * otherwise the user simply does not use the application. 



Each user of the free version brings the profit of c × w rubles. Each user of the paid version brings the profit of p rubles.

Your task is to help the application developers to select the optimal parameters p and c. Namely, knowing all the characteristics of users, for each value of c from 0 to (max bi) + 1 you need to determine the maximum profit from the application and the corresponding parameter p.

Input

The first line contains two integers n and w (1 ≤ n ≤ 105; 1 ≤ w ≤ 105) — the number of users and the profit from a single banner. Each of the next n lines contains two integers ai and bi (0 ≤ ai, bi ≤ 105) — the characteristics of the i-th user.

Output

Print (max bi) + 2 lines, in the i-th line print two integers: pay — the maximum gained profit at c = i - 1, p (0 ≤ p ≤ 109) — the corresponding optimal app cost. If there are multiple optimal solutions, print any of them.

Examples

Input

2 1
2 0
0 2


Output

0 3
3 2
4 2
2 2


Input

3 1
3 1
2 2
1 3


Output

0 4
3 4
7 3
7 2
4 2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int inf = 0x7fffffff;
const double eps = 1e-10;
const double pi = acos(-1.0);
const int N = 1e5 + 10;
void read(int &x) {
  int f = 1;
  x = 0;
  char ch;
  ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  x *= f;
}
int n, w, Maxb, Maxa, bel[N], nn, tim[350], q[350][350], qh[350], qt[350];
long long d[N];
struct node {
  int a, b;
} l[N];
double cmp(node a, node b) { return a.b != b.b ? a.b < b.b : a.a > b.a; }
double slope(int i, int j) { return (d[i] - d[j]) * 1.0 / (j - i); }
void add(int x) {
  if (!x) return;
  for (int i = 1; i < bel[x]; ++i) {
    tim[i]++;
    while (qh[i] < qt[i] && slope(q[i][qh[i]], q[i][qh[i] + 1]) <= tim[i])
      ++qh[i];
  }
  int l = (bel[x] - 1) * nn + 1, r = min(bel[x] * nn, Maxa), id = bel[x];
  for (int i = l; i <= r; ++i) d[i] += (long long)tim[id] * i;
  for (int i = l; i <= x; ++i) d[i] += i;
  tim[id] = 0;
  qh[id] = 1;
  qt[id] = 0;
  for (int i = l; i <= r; ++i) {
    while (qh[id] < qt[id] &&
           slope(q[id][qt[id]], i) < slope(q[id][qt[id] - 1], q[id][qt[id]]))
      --qt[id];
    q[id][++qt[id]] = i;
  }
  while (qh[id] < qt[id] && slope(q[id][qh[id]], q[id][qh[id] + 1]) <= 0)
    ++qh[id];
}
int main() {
  read(n);
  read(w);
  for (int i = 1; i <= n; i++)
    read(l[i].a), Maxa = max(Maxa, l[i].a), read(l[i].b),
                  Maxb = max(Maxb, l[i].b);
  sort(l + 1, l + n + 1, cmp);
  int now = 1;
  nn = sqrt(Maxa);
  for (int i = 1; i <= Maxa; i++) bel[i] = (i - 1) / nn + 1;
  int tot = bel[Maxa];
  for (int i = 1; i <= tot; i++) qh[i] = 1, q[i][++qt[i]] = min(i * nn, Maxa);
  for (int c = 0; c <= Maxb + 1; c++) {
    while (now <= n && l[now].b < c) add(l[now].a), ++now;
    long long ans = 0;
    int ans1 = 0;
    for (int i = 1; i <= tot; ++i) {
      int x = q[i][qh[i]];
      if (d[x] + (long long)x * tim[i] > ans)
        ans = d[x] + (long long)x * tim[i], ans1 = x;
    }
    printf("%lld %d\n", ans + (long long)w * c * (n - now + 1), ans1);
  }
  return 0;
}