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 C (GCC 5.4.1) (judge verdict: Runtime Error)

long long dist[1001][1001];
int main(){
	int a,b,t,k,n,i,j;
	long long c;
	scanf("%d%d",&n,&k);
		/*initialize*/
		memset(dist,99,sizeof(dist));
		for(i=1;i<=n;i++)dist[i][i]=0;
		for(;k;k--){
			scanf("%d%d%lld",&a,&b,&c);
			dist[a][b]=dist[b][a]=-c;
		}

		{/*warshall-floyd*/
			int k,i,j;
			for(k=1;k<=n;k++)
				for(i=1;i<=n;i++)
					for(j=1;j<=n;j++)
						if(dist[i][j]>dist[i][k]+dist[k][j])
							dist[i][j]=dist[i][k]+dist[k][j];
		}

		{/*query*/
			for(i=1;i<=n;i++){
				if(dist[i][i]<0){puts("inf");return 0;}
			}
		}
		printf("%lld\n",-dist[1][n]);
}