Problem: Hearing that energy drinks increase rating in those sites, Takahashi decides to buy up M cans of energy drinks.

There are N stores that sell energy drinks. In the i-th store, he can buy at most B_i cans of energy drinks for A_i yen (the currency of Japan) each.

What is the minimum amount of money with which he can buy M cans of energy drinks?

It is guaranteed that, in the given inputs, a sufficient amount of money can always buy M cans of energy drinks.

Constraints

* All values in input are integers.
* 1 \leq N, M \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^5
* B_1 + ... + B_N \geq M

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N


Output

Print the minimum amount of money with which Takahashi can buy M cans of energy drinks.

Examples

Input

2 5
4 9
2 4


Output

12


Input

4 30
6 18
2 5
3 10
7 9


Output

130


Input

1 100000
1000000000 100000


Output

100000000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int main(){
  int N, M;
  cin >> N >> M;
  pair<int,int> A[N];
  for(int i=0;i<N;i++){
    cin >> A[i].first >> A[i].second;
  }
  sort(A, A+N);
  int64_t ans = 0;
  int j = 0;
  for(int i=0;i<M;i++){
    for(j;j<N;j++){
      if(A[j].second > 0){
        ans += A[j].first;
        A[j].second -= 1;
        break;
      }
    }
  }
  cout << ans << endl;
}