// Slower C++ solution:
#pragma region include

#include <iostream>

#include <iomanip>

#include <stdio.h>



#include <sstream>

#include <algorithm>

#include <cmath>

#include <complex>



#include <string>

#include <cstring>

#include <vector>

#include <tuple>



#include <queue>

#include <complex>

#include <set>

#include <map>

#include <stack>

#include <list>



#include <fstream>

#include <random>

//#include <time.h>

#include <ctime>

#pragma endregion //#include

/////////

#define REP(i, x, n) for(int i = x; i < n; ++i)

#define rep(i,n) REP(i,0,n)

/////////

#pragma region typedef

typedef long long LL;

typedef long double LD;

typedef unsigned long long ULL;

#pragma endregion //typedef

////定数

const int INF = (int)1e9;

const LL MOD = (LL)1e9+7;

const LL LINF = (LL)1e18;

const double PI = acos(-1.0);

const double EPS = 1e-9;

/////////

using namespace::std;

/////////

#pragma region Math

#pragma region

template<class T>

inline T gcd(T a, T b){return b ? gcd(b, a % b) : a;}

#pragma endregion // 最大公約数 gcd

#pragma region

template<class T>

inline T lcm(T a, T b){return a / gcd(a, b) * b;}

#pragma endregion // 最小公倍数 lcm

#pragma region

LL powMod(LL num,LL n,LL mod=(LL)MOD){//(num**n)%mod

	num %= mod;//

	if( n == 0 ){

		return (LL)1;

	}

	LL mul = num;

	LL ans = (LL)1;

	while(n){

		if( n&1 ){

			ans = (ans*mul)%mod;

		}

		mul = (mul*mul)%mod;

		n >>= 1;

	}

	return ans;

}

#pragma endregion //繰り返し二乗法 powMod

#pragma region

template<class T>

vector<T> getDivisor(T n){

	vector<T> v;

	for(int i=1;i*i<=n;++i){

		if( n%i == 0 ){

			v.push_back(i);

			if( i != n/i ){//平方数で重複して数えないように

				v.push_back(n/i);

			}

		}

	}

	sort(v.begin(), v.end());

	return v;

}

#pragma endregion //約数列挙 getDivisor(n):O(√n)

#pragma endregion //math

//Utility:便利な奴

#pragma region

template<class T>

void UNIQUE(vector<T>& vec){

	sort(vec.begin(),vec.end());

	vec.erase(unique(vec.begin(),vec.end()),vec.end() );

}

#pragma endregion // sort erase unique

////////////////////////////////

#pragma region 

long long  bitcount64(long long bits)

{

    bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);

    bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);

    bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);

    bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);

    bits = (bits & 0x0000ffff0000ffff) + (bits >>16 & 0x0000ffff0000ffff);

    return (bits & 0x00000000ffffffff) + (bits >>32 & 0x00000000ffffffff);

}

#pragma endregion //その他

////////////////////////////////

struct edge_base{int to;LL cost;};

edge_base make_edge_base(int to,LL cost){

	edge_base ret = {to,cost};

	return ret;

}

#pragma region GRL

#pragma region //グラフ

template<class T,class EDGE>

void dijkstra(int root,int V,vector<T>& dist,

	vector< vector<EDGE> > G	){

	priority_queue<pair<T,int>,vector<pair<T,int> >,greater<pair<T,int> > > que;

	dist.assign(V,LINF);

	dist[root] = 0;

	que.push(pair<T,int>(0,root));//距離、頂点番号



	while( !que.empty() ){

		pair<T,int> p = que.top();que.pop();

		int v = p.second;

		if( dist[v] < p.first ) continue;

		for(int i=0;i < (int)G[v].size();++i){

			EDGE e = G[v][i];

			if( dist[e.to] > dist[v] + e.cost ){

				dist[e.to] = dist[v] + e.cost;

				que.push(pair<T,int>(dist[e.to],e.to));

			}

		}

	}

}

#pragma endregion //ダイクストラ法:O(|E|log|V|)

#pragma region //グラフ

void warshall_floyd(vector<vector<LL> >& dist,int V,const LL inf=LINF){

	for(int k=0;k<V;++k){

		for(int i=0;i<V;++i){

			if( dist[i][k] >= inf ) continue;

			for(int j=0;j<V;++j){

				if( dist[k][j] >= inf )continue;

				dist[i][j] = min(dist[i][j],dist[i][k]+dist[k][j]);

			}

		}

	}

}

#pragma endregion //ワーシャルフロイド:O(|V|**3)

#pragma region

namespace FLOW{

//vector< vector<FLOW:edge> > G;



struct edge_flow : public edge_base{

	LD cap;//int cap;

	int rev;

};

//edge_flow make_edge_flow(int to,int cap,int rev,LL cost=1){

edge_flow make_edge_flow(int to,LD cap,int rev,LL cost=1){

	edge_flow ret;

	

	ret.to = to;

	ret.cost = cost;

	ret.cap = cap;

	ret.rev = rev;

	return ret;

}



/*

class Graph{

public:

	int V;

	vector< vector<FLOW::edge_flow> > G;

	vector< LL > dist;

	vector< int > iter;

	void init(int v){

		V = v;

		G.resize(V);

	}

	//directed graph

	void add_edge(int from,int to,int cap){

		G[from].push_back( FLOW::make_edge_flow(to,cap,G[to].size()) );

		G[to].push_back( FLOW::make_edge_flow(from,0,G[from].size()-1) );

	}

	

private:

	//sから最短距離をBFSで計算する

	void bfs(int s){//許容量もチェックしている

		queue<int> que;

		dist = vector<LL>(V,-1);

		dist[s] = 0;

		que.push(s);

		while(!que.empty()){

			int v = que.front();que.pop();

			for(int i=0;i<(int)G[v].size();++i){

				edge_flow &e = G[v][i];

				if( e.cap > 0 && dist[e.to] < 0 ){

					dist[e.to] = dist[v] + 1;

					que.push(e.to);

				}

			}

		}

	}

private:

	//増加パスをDFSで探す

	int dfs(int v,int t,int f){

		if( v==t ) return f;

		for(int &i = iter[v];i<(int)G[v].size();++i){//?

			FLOW::edge_flow &e = G[v][i];

			if( e.cap>0 && dist[v] < dist[e.to]){

				int d = this->dfs(e.to, t, min(f,e.cap) );

				if( d > 0){

					e.cap -= d;

					G[e.to][e.rev].cap += d;

					return d;

				}

			}

		}

		return 0;

	}

public:

	//sからtへの最大流量を求める

	int max_flow(int s,int t){

		int flow = 0;

		for(;;){

			this->bfs(s);

			if( dist[t] < 0 ) return flow;

			iter = vector<int>(V,0);

			int f;

			while( (f = this->dfs(s,t,INF) ) > 0 ){

				flow += f;

			}

		}

	}

};

//*/

}

#pragma endregion //dinic :O(|E||V|^2)

#pragma region //グラフ

bool is_bipartite(int v,int c,vector< vector<int> >& G,vector<int>& Color){

	Color[v] = c;

	for(int i=0;i < (int)G[v].size();++i){//隣接グラフ

		if(Color[ G[v][i] ] == c ) return false;

		if(Color[ G[v][i] ] == 0 && 

			!is_bipartite(G[v][i],-c,G,Color)

			){

				return false;

		}

	}

	return true;

}

bool is_bipartite(int Root,vector< vector<int> >& Graph){

	int GraphSize = Graph.size();

	vector<int> Color(GraphSize,0);

	const int ColorNo = 1;

	return is_bipartite(Root,ColorNo,Graph,Color);

}

#pragma endregion //二部グラフチェック is_bipartite(root,GraphList)

#pragma endregion //

#pragma region 

vector< vector<LL> > NCK;//初期値:0

//http://sugarknri.hatenablog.com/entry/2016/07/16/165715

void makeinv(vector<LL>& inv,const LL P){

	int i;

	const int varMAX = 100000;

	inv = vector<LL>( varMAX+1,0);

	inv[1]=1;

	for(i=2;i<=varMAX;i++){

		inv[i] = (inv[P%i] * (P-P/i)%P ) % P;//OVF

		//inv[i] = powMod(i,P-2,P);

	}

}



LL nCk(LL N,LL k,LL mod = MOD){

	static vector<LL> inv;//modの逆元

	if( inv.size() == 0 ){

		makeinv(inv,mod);//modは素数を入れる

	}

	k = min(k,N-k);

	if( k < 0 || k > N){return 0;}

	if( k == 0 ){return 1;}

	if( k == 1 ){return N%mod;}

	LL ret = 1;

	for(int i=1;i<=k;++i){

		ret = (ret * ((N+1-i)%mod) )%mod;//ret*N:OVF

		ret = (ret * inv[i] )%mod;

		//ret *= ((N+1-i)*inv[i])%mod;//OVF

		//ret %= mod;

	}

	return ret;

}

LL nCk_once(LL N,LL k,LL mod = MOD){//modは素数

	k = min(k,N-k);

	if( k < 0 || k > N ){return 0;}

	if( k == 0 ){return 1;}

	if( k == 1 ){return N%mod;}

	LL ret = 1;

	LL A=1;

	for(LL i=0;i<k;++i){

		A = (A * ((N-i)%mod) ) % mod;

	}

	LL B=1;

	for(LL i=2;i<=k;++i){

		B = (B * (i%mod) ) % mod;

	}

	ret = ( A * powMod(B,mod-2,mod) ) % mod;

	return ret;

}

#pragma endregion //組み合わせnCk(,10^5)

#pragma region



LL nCk_base(int N,int K,LL mod=MOD){

	if( K<0 || N < K ) return 0;//多く取り過ぎ

	K = min(K,N-K);

	if( K==0 ){return 1%mod;}

	if( K==1 ){return N%mod;}//%MOD;

	if( N<=10000 && NCK[N][K] ){

		return NCK[N][K];

	}

	//N個目を使わない:nCk(N-1,k)

	//N個目を使う	:nCk(N-1,k-1)

	LL ans = (nCk_base(N-1,K)+nCk_base(N-1,K-1) )%mod;//%MOD;

	if( N<=10000 ){

		NCK[N][K] = ans;

	}

	return ans;

}



#pragma endregion //組み合わせ メモ?

#pragma region CGL

class Point{

public:

	double x,y;

	Point(double x=0,double y=0):x(x),y(y){}



	Point	operator +	(Point p){return Point(add(x,p.x),add(y,p.y));}

	void	operator +=	(Point p){x=add(x,p.x);y=add(y,p.y);}

	Point	operator -	(Point p){return Point(add(x,-p.x),add(y,-p.y));}

	void	operator -=	(Point p){x=add(x,-p.x);y=add(y,-p.y);}

	Point	operator *	(double a){return Point(x*a,y*a);}

	double	operator *	(Point p){return dot(p);}

	Point	operator /	(double a){return Point(x/a,y/a);}



	double norm(){return sqrt(x*x+y*y);}

	double dot(Point p){return add(x*p.x,y*p.y);}

	double rot(Point p){return add(x*p.y,-y*p.x);}

	double add(double a,double b){

		double EPS = 1e-10;

		if( abs(a+b) < EPS*(abs(a)+abs(b)) ){

			return 0;

		}

		return a+b;

	}

};

istream& operator>>(istream& in,Point& P){

	in >> P.x >> P.y;

	return in;

}

bool operator==(Point A,Point B){

	if( A.x==B.x && A.y==B.y)return true;

	return false;

}

bool operator<(Point A,Point B){

	if( A.x < B.x ) return true;

	else if( A.x > B.x ) return false;

	if( A.y < B.y ) return true;

	return false;

}

bool operator>(Point A,Point B){

	if( A<B ) return false;

	if( A==B ) return false;

	return true;

}



//線分で表した直線の交差判定

bool is_cross(Point p1,Point p2,Point q1,Point q2){

	double res = (p2-p1).rot(q2-q1);

	return  res != 0;//平行なら0

}



/*ccwへ//線分p1-p2上に点qがあるか判定

bool on_seg(Point p1,Point p2,Point q){

	return (p1-q).rot(p2-q) == 0 && (p1-q).dot(p2-q) <= 0;

}*/

//直線p1-p2と直線q1-q2の交点

//交差判定をしてから使う:0除算

Point intersection(Point p1,Point p2,Point q1,Point q2){

	return p1+(p2-p1)*((q2-q1).rot(q1-p1)/(q2-q1).rot(p2-p1));

}



//線分ABに対する点C

enum PointPotion{ONLINE_BACK=-2,CLOCKWISE,ON_SEGMENT,COUNTER_CLOCKWISE,ONLINE_FRONT};

PointPotion ccw(Point A,Point B,Point C){

	B -= A;C -=A;

	if( B.rot(C) > 0 ) return COUNTER_CLOCKWISE;//+1

	if( B.rot(C) < 0 ) return CLOCKWISE;//-1

	if( B.dot(C) < 0 ) return ONLINE_BACK;//-2

	if( B.norm() < C.norm() ) return ONLINE_FRONT;//+2

	return ON_SEGMENT;//0

}

//線分p1-p2,と線分q1-q2の交差判定

//http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B

bool intersect(Point p1,Point p2,Point q1,Point q2){

	return	(ccw(p1,p2,q1) * ccw(p1,p2,q2) <= 0) &&

			(ccw(q1,q2,p1) * ccw(q1,q2,p2) <= 0);

}

///

//直線p1-p2と点q1の距離

double dist_LineP(Point p1,Point p2,Point q1){

	return abs( (p2-p1).rot(q1-p1) )/(p2-p1).norm();

}

//線分p1-p2と点q1の距離

double dist_SegP(Point p1,Point p2,Point q1){

	//(日)

	if( (p2-p1).dot(q1-p1) < 0 ){

		return (q1-p1).norm();//p1から見てp2と逆方向

	}

	if( (p1-p2).dot(q1-p2) < 0 ){

		return (q1-p2).norm();//p2から見てp1と逆方向

	}

	return dist_LineP(p1,p2,q1);//垂線下ろす

}

// 線分同士の最短距離

//http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D

//http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=862507#1

double dist_segseg(Point A1,Point A2,Point B1,Point B2){

	if( intersect(A1,A2,B1,B2) ){

		return 0;

	}

	return min(

		min(dist_SegP(A1,A2,B1),

			dist_SegP(A1,A2,B2)

			),

		min(dist_SegP(B1,B2,A1),

			dist_SegP(B1,B2,A2)

			)

		);

}

#pragma endregion //class Point

#pragma region CGL

//多角形内なら2,線上なら1,外なら0

//http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C

//http://www.prefield.com/algorithm/geometry/contains.html

//点Pから半直線を引く、ガウス

int contains(vector<Point>& v,Point& P){

	bool in = false;

	const int N = v.size();

	for(int i=0;i<N;++i){

		Point A = (v[i]-P);

		Point B = (v[(i+1)%N]-P);

		if( A.y > B.y ) swap(A,B);

		if( A.y <= 0 && 0 < B.y ){

			if( A.rot(B) < 0 ) in =!in;

		}

		if( A.rot(B) == 0 && A.dot(B) <= 0 ){

			return 1;//ON 線上

		}

	}

	return in ? 2:0;//中:外

}

#pragma endregion //contains

#pragma region CGL

//辞書順で比較

bool cmp_x(const Point& p,const Point& q){

	if( p.x != q.x ) return p.x < q.x;

	return p.y < q.y;

}



//凸包を求める

vector<Point> convex_hull(vector<Point> ps,int n){

	sort(ps.begin(),ps.end(), cmp_x);

	int k = 0;//凸包の頂点数

	vector<Point> qs(n*2);//構築中の凸包

	//下側の凸包の作成

	for(int i=0;i<n;++i){

		while(k>1 && (qs[k-1]-qs[k-2]).rot(ps[i]-qs[k-1]) <=0){//<で線上も加える

			k--;

		}

		qs[k++] = ps[i];

	}

	//上側凸包の作成

	for(int i=n-2,t=k;i>=0;i--){

		while(k>t && (qs[k-1]-qs[k-2]).rot(ps[i]-qs[k-1]) <=0){//<

			k--;

		}

		qs[k++] = ps[i];

	}

	qs.resize(k-1);

	return qs;

}

#pragma endregion //凸包

#pragma region DSL

#pragma region DSL

class UnionFind{

public:

	int cNum;//要素数

	vector<int> parent;

	vector<int> count;

	vector< vector<int> > GList;

	UnionFind(int n){

		cNum = n;

		parent = vector<int>(n);

		count = vector<int>(n,1);

		GList.resize(n);

		for(int i=0;i<n;++i){

			parent[i] = i;

			GList[i].push_back(i);

		}

	}

	int find(int x){

		if( parent[x] == x ){return x;}

		return parent[x] = find( parent[x] );

	}

	bool same(int x,int y){return find(x) == find(y);}

	int Count(int x){return count[find(x)];}

	void add(int x,int y){//union

		x = find(x);

		y = find(y);

		if( x==y )return;

		parent[x] = y;

		

		count[y] += count[x];

		if( GList[y].size() < GList[x].size() ){

			swap(GList[x],GList[y]);

		}

		GList[y].insert( GList[y].end(),

			GList[x].begin(),GList[x].end() );

	}

};



#pragma endregion //UnionFind

#pragma region DSL

class segment{

	int n;

	int OTHER_VAL;

	int NUM_NULL;

	vector< int > dat;

public:

	int getN(){return n;}

	void init(int size,int num=INF,int num_null=-1){//N:要素数,最大値

		OTHER_VAL = num;

		NUM_NULL = num_null;

		n = 2;

		while(n < size ){

			n <<= 1;

		}

		dat.assign(n<<1, OTHER_VAL );

	}

	void init(vector<int> vec,int size,int num=INF){

		OTHER_VAL = num;

		n = 2;

		while(n < size ){

			n <<= 1;

		}

		dat.assign(n<<1,OTHER_VAL );

		for(int i=0;i<size;++i){

			update(i,vec[i]);

		}

	}

	int SELECT(int L,int R){

		return min(L,R);

	}

	void update(int i,int x){

		i += n;

		while(i){

			dat[i] = SELECT(dat[i],x);

			i >>= 1;

		}

	}

	void update(int X,int Y,int VAL){

		//全体の範囲は閉区間、

		update(1,0,n-1,X,Y,VAL);

	}

private:

	void update(int t,int L,int R,int X,int Y,int VAL){

		//親から子へ進んでいく

		if( L == X && R == Y){

			dat[t] = VAL;

		}else{

			int mid = (L+R)/2;

			if( dat[t] != NUM_NULL ){//値の伝播

				dat[t*2+0] = dat[t];

				dat[t*2+1] = dat[t];

				dat[t] = NUM_NULL;

			}

			if( Y <= mid ){

				update(t*2+0,L,mid,X,Y,VAL);

			}else if( X > mid ){

				update(t*2+1,mid+1,R,X,Y,VAL);

			}else{

				update(t*2+0,L,mid,X,mid,VAL);

				update(t*2+1,mid+1,R,mid+1,Y,VAL);

			}

		}

	}

public:

	//query(a,b,0,0,n)//[a,b)半開区間

	int query(int a,int b){

		return query(a,b,1,0,n);//n==getNを使う

	}

private:

	int query(int a,int b,int k,int l,int r){

		if(r<=a || b<=l)return OTHER_VAL;//交差しない

		if(a<=l && r<=b && dat[k]!=NUM_NULL)return dat[k];



		int res = OTHER_VAL;

		int mid = (l+r)>>1;

		if( a < mid ) res = SELECT(res,query(a,b,k*2+0,l,mid) );

		if( mid < b ) res = SELECT(res,query(a,b,k*2+1,mid,r) );

		return res;

	}

};

/*

segment_base<LL> LL_seg;

0-index

*/

template <typename T>

class segment_base{

	int N;//要素数

	vector< T > dat1;

	T VAL_E;//初期値

public:

	segment_base(int n,T val_E ):N(n),VAL_E(val_E){

		dat1.resize(2*n);

		dat1.assign(2*n,val_E);//初期化

	}

	void init(int n,T val_E){

		N = n;

		VAL_E = val_E;

		dat1.resize(2*n);

		dat1.asigne(2*n,val_E);

	}

	T SELECT(T L,T R){//扱う演算子

		T ans;

		ans = L+R;//

		return ans;

	}



	//index番目の値をvalに変更,indexは"0-index"

	void update(int index,T val){

		for(dat1[index+=N] = val;index>1;index>>=1){

			dat1[index>>1] = SELECT(dat1[index],dat1[index^1]);//index+0,+1

		}

	}



	//区間[L,R)のSELECT

	T query(int L,int R){

		T ans = VAL_E;//

		for(L+=N,R+=N; L<R;L>>=1,R>>=1){

			if(L&1) ans = SELECT(ans,dat1[L++]);

			if(R&1) ans = SELECT(ans,dat1[--R]);

		}

		return ans;

	}

	///////////////

	//区間[L,R)に足す

	void modify(int L,int R, T val){

		for(L+=N,R+=N;L<R;L>>=1,R>>=1){

			if(L&1) {dat1[L] += val;L++;}

			if(R&1) {--R;dat1[R] += val;}

		}

	}

	T acc(int index){

		T ans = VAL_E;///

		for( index+=N;index>0;index>>=1){

			ans = SELECT(ans,dat1[index]);

		}

		return ans;

	}

};

#pragma endregion //segment tree

#pragma region DSL

class BITree{//1-index

	int N;

	vector<LL> bit;

public:

	BITree(int n){

		N = n;

		bit = vector<LL>(N+1,0);//1-index

	}

	void add(int a,LL w){//aにwを足す

		if( a <= 0 || N < a) return;//a:[1,N]

		for(int i=a;i<=N;i += i & -i){

			bit[i] += w;

		}

	}

	LL sum(int a){//[1,a]の和,a:[1,N]

		/*

		1番目からa番目までの和、1-index

		*/

		LL ret = 0;

		if( a > N ) a = N;

		for(int i=a; i > 0; i -= i & -i){

			ret += bit[i];

		}

		return ret;

	}

};

#pragma endregion //BIndexTree



#pragma region 

template<class T,class U>

istream& operator>>(istream& in,pair<T,U>& P){

	in >> P.first >> P.second;

	return in;

}

#pragma endregion //cin pair<T,U>

#pragma region 

template<class T>

istream& operator>>(istream& in,vector<T>& v){

	int size = v.size();

	for(int i=0;i<size;++i){

		in >> v[i];

	}

	return in;

}

#pragma endregion //cin vector<int>

#pragma region 

//行列の積

template<class T>

vector< vector<T> > operator*( vector<vector<T> >& A,vector< vector<T> >& B){

	LL mod = MOD;

	int R = A.size();

	int cen = A[0].size();

	int C = B[0].size();

	vector< vector<T> > ans(R,vector<T>(C,0) );

	for(int row=0;row<R;++row){

		for(int col=0;col<C;++col){

			for(int inner=0;inner< cen;++inner){

				ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col])%mod;

				//ans[row][col] = (ans[row][col] + A[row][inner]*B[inner][col]);

			}

		}

	}

	return ans;

}



template<class T>

vector< vector<T> > powMod(vector< vector<T> > mat,LL N){

	int R = mat.size();

	int C = mat[0].size();

	//R==C

	vector< vector<T> > I(R,vector<T>(C,0));//単位元

	for(int i=0;i<R && i<C;++i){

		I[i][i] = 1;

	}

	if( N == 0 ){

		return I;

	}

	vector< vector<T> > mul(R,vector<T>(C)),ans(R,vector<T>(C));

	ans = I;

	mul = mat;

	while(N){

		if( N & 1 ){

			ans = ans*mul;

		}

		N >>= 1;

		mul = mul*mul;

	}

	return ans;

}

#pragma endregion //行列



#pragma region

namespace TIME{

time_t start,limit;

void time_start(){start = time(NULL);}

void time_set(int num){limit = num;}//秒

bool check(){return (time(NULL)-start < limit);}

}

#pragma endregion //時間計測

/*

#pragma region

namespace RAND{

mt19937 mt;

void rand_init(){

	random_device rnd;

	mt = mt19937(rnd());

}

int rand(){

	return mt();

}

}

#pragma endregion //乱数

*/

#pragma region

#pragma endregion //

////////////////////

#pragma region

double area(vector<Point> poly){

	int size = poly.size();

	double ans = 0;

	for(int i=1;i<size-1;++i){

		ans += (poly[i]-poly[0]).rot(poly[i+1]-poly[0])/2;

	}

	return ans;

}

#pragma endregion //多角形の面積

////////////////////

#pragma region CGL

bool compare_x(Point A,Point B){

	return A.x < B.x;

}

bool compare_y(Point A,Point B){

	return A.y < B.y;

}

//vecはx座標の昇順で渡される

double closest_pair(vector<Point>::iterator itr,int N){

	if(  N <= 1 ) return INF;

	int m = N/2;

	double x = (itr+m)->x;

	double d = min(closest_pair(itr,m),

		closest_pair((itr+m),N-m) );

	

	inplace_merge(itr,itr+m,itr+N,compare_y);



	vector<Point> B;

	for(int i=0;i<N;++i){

		if(fabs((itr+i)->x - x) >= d) continue;

		int Bsize = B.size();

		for(int j=0;j<Bsize;j++){

			double dx,dy;

			dx = (itr+i)->x - B[Bsize-j-1].x;

			dy = (itr+i)->y - B[Bsize-j-1].y;

			if( dy >= d ) break;

			d = min(d,hypot(dx,dy));

		}

		B.push_back(*(itr+i));

	}

	return d;

}

#pragma endregion //最近対 2D

////////////////////

#pragma region

int CircleIntersection(Point A,double AR,Point B,double BR){

	double D = (B-A).norm();

	if( D > AR+BR ){

		return 4;

	}else if( D == AR+BR ){

		return 3;

	}else if( abs(AR-BR) < D  ){//&& D<AR+BR

		return 2;

	}else if(D == abs(AR-BR)){

		return 1;

	}else if(D+AR < BR || D+BR<AR){

		return 0;

	}

	return 0;//

}

#pragma endregion //円と円の位置関係



#pragma region

vector<Point> CircleLine(Point C,double CR,Point A,Point B){

	vector<Point> ans(2);//同じ交点なら同じ値

	double a,b,c;

	a = -(A.y-B.y);

	b = A.x-B.x;

	c = -(a*A.x+b*A.y);



	double l,k,d;

	l = a*a+b*b;

	k = a*C.x + b*C.y+ c;

	d = l*CR*CR-k*k;

	if(d>0){

		double ds = sqrt(d);

		double apl = a/l;

		double bpl = b/l;

		double xc = C.x-apl*k;

		double yc = C.y-bpl*k;

		double xd = bpl*ds;

		double yd = apl*ds;

		Point temp;

		ans[0].x = xc-xd;

		ans[0].y = yc+yd;

		ans[1].x = xc+xd;

		ans[1].y = yc-yd;

	}else if(d==0){

		Point temp;

		temp.x = C.x-a*k/l;

		temp.y = C.y-b*k/l;

		ans[0] = temp;

		ans[1] = temp;

	}else{

		Point temp;

		temp.x = INF;

		temp.y = INF;

		ans[0] = temp;

		ans[1] = temp;

	}

	return ans;

}

#pragma endregion //円と直線の交点,距離チェックする。

//////////////////

//行列式

/////////////////

const int MAX = 100000;

vector<LL> ans(MAX+1,0);

vector<LL> sum(MAX+1,0);

 

void solve(){

	LL N,K;

	cin >> N >> K;

	

	int pos = 0;

	for(int i=0;i<N;++i){

		LL a,b;

		cin >> a >> b;

		ans[(int)a] += b;

	}

	for(int i=1;i<=MAX;++i){

		sum[i] = sum[i-1] + ans[i];

	}

	LL index = lower_bound(sum.begin(), sum.end(),K) -sum.begin();

	cout << index << endl;

}



#pragma region main

signed main(void){

	std::cin.tie(0);

	std::ios::sync_with_stdio(false);

	std::cout << std::fixed;//小数を10進数表示

	cout << setprecision(16);//小数点以下の桁数を指定//coutとcerrで別	

	

	solve();

}

#pragma endregion //main()


// Faster C++ solution for the same problem (measured speedup: 2.7971370414971157x):
#pragma region include

#include <iostream>

#include <iomanip>

#include <stdio.h>



#include <sstream>

#include <algorithm>

#include <cmath>

#include <complex>



#include <string>

#include <cstring>

#include <vector>

#include <tuple>



#include <queue>

#include <complex>

#include <set>

#include <map>

#include <stack>

#include <list>



#include <fstream>

#include <random>

//#include <time.h>

#include <ctime>

#pragma endregion //#include

/////////

#define REP(i, x, n) for(int i = x; i < n; ++i)

#define rep(i,n) REP(i,0,n)

/////////

#pragma region typedef

typedef long long LL;

typedef long double LD;

typedef unsigned long long ULL;

#pragma endregion //typedef

////定数

const int INF = (int)1e9;

const LL MOD = (LL)1e9+7;

const LL LINF = (LL)1e18;

const double PI = acos(-1.0);

const double EPS = 1e-9;

/////////

using namespace::std;

 

void solve(){

	int N;

	LL K;

	cin >> N >> K;

	vector< pair<int,int> > v;

	for(int i=0;i<N;++i){

		int a,b;

		cin >> a >> b;

		v.push_back(pair<int,int>(a,b) );

	}

	sort( v.begin(), v.end() );

	LL sum = 0;

	for(int i=0;i<N;++i){

		sum += v[i].second;

		if( K <= sum ){

			cout << v[i].first << endl;

			return;

		}

	}

	

}



#pragma region main

signed main(void){

	std::cin.tie(0);

	std::ios::sync_with_stdio(false);

	std::cout << std::fixed;//小数を10進数表示

	cout << setprecision(16);//小数点以下の桁数を指定//coutとcerrで別	

	

	solve();

}

#pragma endregion //main()