Problem:
RMQ and RAQ

Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations:

$add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$.

$find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$.

Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0.

Input

$n$ $q$
$query_1$
$query_2$
:
$query_q$

In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format:

0 $s$ $t$ $x$

or

1 $s$ $t$

The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$.

Output

For each $find$ query, print the minimum value.

Constraints

$1 ≤ n ≤ 100000$

$1 ≤ q ≤ 100000$

$0 ≤ s ≤ t < n$

$-1000 ≤ x ≤ 1000$

Sample Input 1

6 7
0 1 3 1
0 2 4 -2
1 0 5
1 0 1
0 3 5 3
1 3 4
1 0 5

Sample Output 1

-2
0
1
-1

Solution in C++11 (judge verdict: Accepted)

   #include <bits/stdc++.h>
 
//    #include <boost/multiprecision/cpp_int.hpp>
 #define int long long
 #define inf  1000000007
// #define inf  998244353

 #define pa pair<int,int>
 #define ll long long
 #define pal pair<double,double>
 #define ppap pair<pa,int>
  #define PI 3.14159265358979323846
  #define paa pair<int,char>
  #define  mp make_pair
  #define  pb push_back
  #define EPS (1e-8)
                                          
    int dx[8]={0,1,0,-1,1,1,-1,-1};
    int dy[8]={1,0,-1,0,-1,1,1,-1};
                                            using namespace std;
                                   			class pa3{
                                            	public:
                                            	int x;
                                   				int y,z;
                                            	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                            	bool operator < (const pa3 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		 return z<p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                   				bool operator > (const pa3 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		 return z>p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa3 &p) const{
                                            		return x==p.x && y==p.y && z==p.z;
                                            	}
                                            		bool operator != (const pa3 &p) const{
                                            			return !( x==p.x && y==p.y && z==p.z);
                                            	}
                                            
                                            };
                                            
                                            class pa4{
                                            	public:
                                            	int x;
                                            	int y,z,w;
                                            	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                            	bool operator < (const pa4 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		if(z!=p.z)return z<p.z;
                                            		return w<p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator > (const pa4 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		if(z!=p.z)return z>p.z;
                                            		return w>p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa4 &p) const{
                                            		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                            	}
                                            		
                                            
                                            };
                                            class pa2{
                                            	public:
                                            	int x,y;
                                            	pa2(int x=0,int y=0):x(x),y(y) {}
                                            	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                            	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                            	bool operator < (const pa2 &p) const{
                                            		return y != p.y ? y<p.y: x<p.x;
                                            	}
                                            	bool operator > (const pa2 &p) const{
                                            		return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa2 &p) const{
                                            		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                            	}
                                            	bool operator != (const pa2 &p) const{
                                            		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                            	}
                                            		
                                            
                                            };
                                            
 
                      
                                string itos( int i ) {
                                ostringstream s ;
                                s << i ;
                                return s.str() ;
                                }
                                 
                                int Gcd(int v,int b){
                                	if(v==0) return b;
                                	if(b==0) return v;
                                	if(v>b) return Gcd(b,v);
                                	if(v==b) return b;
                                	if(b%v==0) return v;
                                	return Gcd(v,b%v);
                                }
                 
                            
                                int mod;
int extgcd(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    int d = extgcd(b, a%b, y, x);
    y -= a/b * x;
    return d;
}
pa operator+(const pa & l,const pa & r) {   
    return {l.first+r.first,l.second+r.second};                                    
}    
pa operator-(const pa & l,const pa & r) {   
    return {l.first-r.first,l.second-r.second};                                    
}  
                int beki(int wa,int rr,int warukazu){
                	if(rr==0) return 1%warukazu;
                	if(rr==1) return wa%warukazu;
                	wa%=warukazu;
                	if(rr%2==1) return ((ll)beki(wa,rr-1,warukazu)*(ll)wa)%warukazu;
                	ll zx=beki(wa,rr/2,warukazu);
                	return (zx*zx)%warukazu;
                }
 
                              
                int pr[10];
                int inv[10];
                

                
    			int comb(int nn,int rr){
    				if(rr<0 || rr>nn || nn<0) return 0;
    				int r=pr[nn]*inv[rr];
    				r%=mod;
    				r*=inv[nn-rr];
    				r%=mod;
    				return r;
    			}
               
                void gya(int ert){
                	pr[0]=1;
                	for(int i=1;i<=ert;i++){
                		pr[i]=((ll)pr[i-1]*i)%mod;
                	}
                		inv[ert]=beki(pr[ert],mod-2,mod);
                	for(int i=ert-1;i>=0;i--){
                		inv[i]=(ll)inv[i+1]*(i+1)%mod;
                	}
                }
                
              //   cin.tie(0);
    		//	ios::sync_with_stdio(false);
    			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                 //sort(ve.begin(),ve.end(),greater<int>());
 //   mt19937(clock_per_sec);
  //  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;

struct seg_rangeadd_getmin2{
    //       1
    //   2        3
    // 4   5   6    7
     
     
    private:
    public:
     
    // (1<<15)=32768
    // 1<<16 = 65536
    // 1<<17 = 131072
    // 1<<18 = 262144
     
    int cor=(1<<18);
    int inff=inf*1000000ll;
     
    vector<int> vec;
    vector<int> lazy;
    void shoki1(){
        vec.resize(2*cor+3, 0);
        lazy.resize(2*cor+3, 0);
    }
    void shoki2(){
        //lazy[1]=(1ll<<31)-1;
        //初期値
    }
         
    int chien(int k,int len){
        if(lazy[k]==0) return vec[k];
        if(k<cor){
            vec[k]+=lazy[k];
            lazy[2*k]+=lazy[k];
            lazy[2*k+1]+=lazy[k];
            lazy[k]=0;
        }
        else {
            vec[k]+=lazy[k];
            lazy[k]=0;
        }
    	return vec[k];
    }
	
	void  clear_chien(int r){
		// 1 ~ r までの遅延を開放する
		if(r==0)return;
		int f=31-__builtin_clz(r);
		int pos=0;
		int len=cor;
		for(int i=f;i>=0;i--){
			pos*=2;
			pos+=!!(r&(1<<i));
			chien(pos,len);
			len/=2;
		}
		
	}
	
	void rangeadd(int a,int b,int w){
		a+=cor,b+=cor;
		int aa=a/(a&(-a))/2;
		int bb=b/(b&(-b))/2;
		int lenaa=2*(a&-a);
		int lenbb=2*(b&-b);
		
//	clear_chien(aa);
//	clear_chien(bb);
		while(a<b){
			if(a&1){
				lazy[a]+=w;
				a++;
			}
			if(b&1){
				b--;
				lazy[b]+=w;
			}
			a/=2,b/=2;
		}

		while(aa>0 || bb>0){
			if(aa>bb){
				vec[aa]=min(chien(2*aa,lenaa/2),chien(2*aa+1,lenaa/2));
				aa/=2;		
				lenaa*=2;
			}
			else if(aa<bb){
				vec[bb]=min(chien(2*bb,lenbb/2),chien(2*bb+1,lenbb/2));
				bb/=2;	
				lenbb*=2;
			}
			else{
				vec[aa]=min(chien(2*aa,lenaa/2),chien(2*aa+1,lenaa/2));
				aa/=2;		
				lenaa*=2;
				bb=aa,lenbb=aa;
			}
		}

	}
	
    int getmin(int a,int b){
		a+=cor,b+=cor;
		int aa=a/(a&(-a))/2;
		int bb=b/(b&(-b))/2;
		clear_chien(aa);
		clear_chien(bb);
	
		int ans=inf*1000000000ll;
		
		int len=1;
		while(a<b){
			if(a&1){
				ans=min(ans,chien(a,len));
				a++;
			}
			if(b&1){
				b--;
				ans=min(ans,chien(b,len));
			}
			a/=2,b/=2,len*=2;
		}
		return ans;
	}
     
};
 struct seg_rangeadd_getmin{
    //       1
    //   2        3
    // 4   5   6    7
     
     
    private:
    public:
     
    // (1<<15)=32768
    // 1<<16 = 65536
    // 1<<17 = 131072
    // 1<<18 = 262144
     
    int cor=(1<<18);
    int inff=inf*1000000ll;
     
    vector<int> vec;
    vector<int> lazy;
    void shoki1(){
        vec.resize(2*cor+3, 0);
        lazy.resize(2*cor+3, 0);
    }
    void shoki2(){
        //lazy[1]=(1ll<<31)-1;
        //初期値
    }
         
    void chien(int k,int l,int r){
        //if(lazy[k]==-1) return;
        if(l+1<r){
            vec[k]+=lazy[k];
            lazy[2*k]+=lazy[k];
            lazy[2*k+1]+=lazy[k];
            lazy[k]=0;
        }
        else {
            vec[k]+=lazy[k];
            lazy[k]=0;
        }
    }
     
    int rangeadd(int a,int b,int w, int k=1,int l=0,int r=-3){
        //[a,b)を wに変更
        if(r<0) r=cor;
         
        if(a<=l && r<=b){
            lazy[k]+=w;
            chien(k,l,r);
            return vec[k];
        }
        if(r<=a || b<=l){
            chien(k,l,r);
            return vec[k];
        }
         
        chien(k,l,r);
//  cout<<k<<" "<<l<<" "<<r<<endl;
        int w1=rangeadd(a,b,w,k*2,l,(l+r)/2);
        int w2=rangeadd(a,b,w,k*2+1,(l+r)/2,r);
        vec[k]=min(w1,w2);
        return vec[k];
    }
     
    // [a,b)
    // k-th node
    // k no kukanha [l,r)
     
    int getmin(int a,int b,int k=1,int l=0,int r=-1){
        //[a,b)のminを取得
        if(r<0) r=cor;
        chien(k,l,r);
        if(r<=a || b<=l){// 区間外
            return inff;
        }
         
        if(a<=l && r<=b){// 完全含む
             
            return vec[k];
        }
        int w1=getmin(a,b,k*2,l,(l+r)/2);
        int w2=getmin(a,b,k*2+1,(l+r)/2,r);
        return min(w1,w2);
    }
    void pre(){
        for(int i=1;i<2*cor;i++){
            cout<<vec[i]<<" ";
            if(((i+1)&(-(i+1)))==i+1) cout<<endl;
        }
    }
     
};
 

int rand2(){
	return rand()*rand()&((1<<5)-1);
}
signed main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	
int n,q;
	cin>>n>>q;
seg_rangeadd_getmin ss;
	ss.shoki1();
	for(int i=0;i<q;i++){
		
		int t;
		cin>>t;
		if(t){
			int y,yy;
			cin>>y>>yy;
			cout<<ss.getmin(y,yy+1)<<endl;
		}
		else{
			int y,yy,yyy;
			cin>>y>>yy>>yyy;
			ss.rangeadd(y,yy+1,yyy);
		}
	}
	/*
	//	 seg_addsum_getsum ss;
	seg_rangeadd_getsum ss;
	ss.shoki1();
//	ss2.shoki1();
	
	int ans=0;
	
	ss.rangeadd(10,20,1);
	ss.rangeadd(13,18,3);
	
	cout<<ss.lower_bound(3,26)<<endl;
	
	
	for(int i=0;i<=10000000;i++){
	//	cout<<rand2()<<endl;
		if(rand()&1){
			int l=rand2();
			int r=rand2();
			if(l>r)swap(l,r);
			int v=rand()%100;
			v-=49;
	//		cout<<v<<endl;
			ss.rangeadd(l,r,v);
			ss2.rangeadd(l,r,v);
			
			
		}
		else{
			int l=rand2();
			int r=rand2();
			if(l>r)swap(l,r);
			if(ss2.getsum(l,r)!=ss.getsum(l,r))cout<<"!!!"<<endl;
			
		}
	}
*/
	
	return 0;
 }