Problem: You are given an integer N. Consider an infinite N-ary tree as shown below:

<image>

Figure: an infinite N-ary tree for the case N = 3

As shown in the figure, each vertex is indexed with a unique positive integer, and for every positive integer there is a vertex indexed with it. The root of the tree has the index 1. For the remaining vertices, vertices in the upper row have smaller indices than those in the lower row. Among the vertices in the same row, a vertex that is more to the left has a smaller index.

Regarding this tree, process Q queries. The i-th query is as follows:

* Find the index of the lowest common ancestor (see Notes) of Vertex v_i and w_i.

Constraints

* 1 ≤ N ≤ 10^9
* 1 ≤ Q ≤ 10^5
* 1 ≤ v_i < w_i ≤ 10^9

Input

Input is given from Standard Input in the following format:


N Q
v_1 w_1
:
v_Q w_Q


Output

Print Q lines. The i-th line (1 ≤ i ≤ Q) must contain the index of the lowest common ancestor of Vertex v_i and w_i.

Examples

Input

3 3
5 7
8 11
3 9


Output

2
1
3


Input

100000 2
1 2
3 4


Output

1
1

Solution (in CPP):

Solution:
                                        #include <bits/stdc++.h>
                                        #include<iostream>
                                        #include<cstdio>
                                        #include<vector>
                                        #include<queue>
                                        #include<map>
                                        #include<cstring>
                                        #include<string>
                                        #include <math.h>
                                        #include<algorithm>
                                    //    #include <boost/multiprecision/cpp_int.hpp>
                                        #include<functional>
                               #define int long long
                                        #define inf  10000000000007
                                        #define pa pair<int,int>
                                        #define ll long long
                                        #define pal pair<double,pa>
                                        #define ppa pair<pa,int>
                                        #define ppap pair<int,pa>
                                        #define ssa pair<string,int>
                                        #define  mp make_pair
                                        #define  pb push_back
                                        #define EPS (1e-10)
                                        #define equals(a,b) (fabs((a)-(b))<EPS)
                                 
                                        using namespace std;
                              
                                        class Point{
                                        	public:
                                        	double x,y;
                                        	Point(double x=0,double y=0):x(x),y(y) {}
                                        	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                        	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
                                        	Point operator * (double a) {return Point(x*a,y*a);}
                                        	Point operator / (double a) {return Point(x/a,y/a);}
                                        	double absv() {return sqrt(norm());}
                                        	double norm() {return x*x+y*y;}
                                        	bool operator < (const Point &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const Point &p) const{
                                        		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                        	}
                                        };
                                        typedef Point Vector;
                                 
                                        struct Segment{
                                        Point p1,p2;
                                        };
                                         double dot(Vector a,Vector b){
                                        	return a.x*b.x+a.y*b.y;
                                        }
                                        double cross(Vector a,Vector b){
                                        	return a.x*b.y-a.y*b.x;
                                        }
                                    
            bool parareru(Point a,Point b,Point c,Point d){
            //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
            	return abs(cross(a-b,d-c))<EPS;
            }
            double distance_ls_p(Point a, Point b, Point c) {
              if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
              if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
              return abs(cross(b-a, c-a)) / (b-a).absv();
            }
            bool is_intersected_ls(Segment a,Segment b) {
            	if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2) return false;
            	if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
            //		cout<<"sss"<<endl;
            		if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
            		if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
            		if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
            		if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
            		return false;
            	}
              else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1, b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1, a.p2-b.p1) < EPS );
            }
             
            double segment_dis(Segment a,Segment b){
            	if(is_intersected_ls(a,b))return 0;
            	double r=distance_ls_p(a.p1, a.p2, b.p1);
            	r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
            	return r;
            }
            Point intersection_ls(Segment a, Segment b) {
              Point ba = b.p2-b.p1;
              double d1 = abs(cross(ba, a.p1-b.p1));
              double d2 = abs(cross(ba, a.p2-b.p1));
              double t = d1 / (d1 + d2);
             
              return a.p1 + (a.p2-a.p1) * t;
            }
             
                            string itos( int i ) {
                            ostringstream s ;
                            s << i ;
                            return s.str() ;
                            }
                             
                            int gcd(int v,int b){
                            	if(v>b) return gcd(b,v);
                            	if(v==b) return b;
                            	if(b%v==0) return v;
                            	return gcd(v,b%v);
                            }
             
                            double distans(double x1,double y1,double x2,double y2){
                            	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                            	return sqrt(rr);
                            	
                            }
                            /*
            int pr[100010];
            //int inv[100010];
            */ 
            int beki(int wa,int rr,int warukazu){
            	if(rr==0) return 1ll;
            	if(rr==1) return wa%warukazu;
            	if(rr%2==1) return (beki(wa,rr-1,warukazu)*wa)%warukazu;
            	int zx=beki(wa,rr/2,warukazu);
            	return (zx*zx)%warukazu;
            }
              /*
            void gya(){
            	pr[0]=1;
            	for(int i=1;i<100010;i++){
            		pr[i]=(pr[i-1]*i)%inf;
            	}
            	for(int i=0;i<100010;i++) inv[i]=beki(pr[i],inf-2);
            	
            }
             
            */
             //sort(ve.begin(),ve.end(),greater<int>());
                                     //----------------kokomade tenpure------------
            //vector<double> ans(100000000),ans2(100000000);
            /*
            int par[200100],ranks[200100],kosuu[200100];     
             
            void shoki(int n){
            	for(int i=0;i<n;i++){
            		par[i]=i;
            		ranks[i]=0;
            		kosuu[i]=1;
            	}
            }
             
            int root(int x){
            	return par[x]==x ? x : par[x]=root(par[x]);
            }
             
            bool same(int x,int y){
            return root(x)==root(y);
            }
             
            void unite(int x,int y){
             x=root(x);
             y=root(y);
            	int xx=kosuu[x],yy=kosuu[y];
             if(x==y) return;
            	if(ranks[x]<ranks[y]){
            		par[x]=y;
            		kosuu[y]=yy+xx;
            	}
             else {
            	par[y]=x;
            	if(ranks[x]==ranks[y]) ranks[x]=ranks[x]+1;
             	kosuu[x]=yy+xx;
             }
            	return;
            }
            */
         
     
        signed main(){
         //if(i%k==0) cout<<endl;
        	
      int n;
        	cin>>n;
        	
        	int qu;
        	cin>>qu;
        	
        	for(int i=0;i<qu;i++){
        		
        		
        		int u,v;
        		cin>>u>>v;
        		if(n==1){
                  cout<<min(u,v)<<endl;
                  continue;
                }
        		while(u!=v){
        			if(u>=v){
        				u=(u+n-2)/n;
        			}
        			else v=(v+n-2)/n;
        		}
        		cout<<u<<endl;
        	}
        	
        	
        	return 0;
        }