Problem:
Score : 300 points

Problem Statement

There is an empty array.
The following N operations will be performed to insert integers into the array.
In the i-th operation (1≤i≤N), b_i copies of an integer a_i are inserted into the array.
Find the K-th smallest integer in the array after the N operations.
For example, the 4-th smallest integer in the array \{1,2,2,3,3,3\} is 3.

Constraints

1≤N≤10^5

1≤a_i,b_i≤10^5

1≤K≤b_1…+…b_n

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
a_1 b_1
:
a_N b_N

Output

Print the K-th smallest integer in the array after the N operations.

Sample Input 1

3 4
1 1
2 2
3 3

Sample Output 1

3

The resulting array is the same as the one in the problem statement.

Sample Input 2

10 500000
1 100000
1 100000
1 100000
1 100000
1 100000
100000 100000
100000 100000
100000 100000
100000 100000
100000 100000

Sample Output 2

1

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
   integer(8) N, K, i
   integer(8), allocatable :: a(:), b(:)
   read(*, *) N, K
   allocate(a(1: N))
   allocate(b(1: N))
   do i = 1, N
       read(*, *) a(i), b(i)
   end do
   call heapsort(N,a,b)

   do i = 1, N
       if(1 <= K .and. K <= b(i)) then
	       write(*, *) a(i)
	       exit
	   else
	       K = K - b(i)
	   end if
   end do
end program main


subroutine heapsort(n,array,arrayb)
  implicit none
  integer(8),intent(in) :: n
  integer(8),intent(inout) :: array(1:n),arrayb(1:n)
  
  integer(8) ::i,k,j,l
  integer(8) :: t, tb
  
  if(n.le.0)then
     write(6,*)"Error, at heapsort"; stop
  endif
  if(n.eq.1)return

  l=n/2+1
  k=n
  do while(k.ne.1)
     if(l.gt.1)then
        l=l-1
        t=array(L)
		tb=arrayb(L)
     else
        t=array(k)
		tb=arrayb(L)
        array(k)=array(1)
		arrayb(k)=arrayb(1)
        k=k-1
        if(k.eq.1) then
           array(1)=t
		   arrayb(1)=tb
           exit
        endif
     endif
     i=l
     j=l+l
     do while(j.le.k)
        if(j.lt.k)then
           if(array(j).lt.array(j+1))j=j+1
        endif
        if (t.lt.array(j))then
           array(i)=array(j)
		   arrayb(i)=arrayb(j)
           i=j
           j=j+j
        else
           j=k+1
        endif
     enddo
     array(i)=t
	 arrayb(i)=tb
  enddo

  return
end subroutine heapsort