#include<bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < n; ++i)
#define rrep(i,n) for (int i = n-1; i >= 0; i--)
#define rep2(i,s,n) for (int i = s; i < n; ++i)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define tmax(a,b,c) max(a,max(b,c))
#define tmin(a,b,c) min(a,min(b,c))
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vvi vector<vector<int>>
#define vl vector<ll>
#define vs vector<string>
#define vc vector<char>
#define vb vector<bool>
#define vp vector<P>
using namespace std;
using ll = long long;
using P = pair<int,int>;
using LP = pair<ll,ll>;
template<class T> istream& operator>>(istream& is,vector<T>& v) { for(T& t:v){is>>t;} return is; }
template<class T> ostream& operator<<(ostream& os,const vector<T>& v) { for(T t:v){os<<t<<" ";} os<<"\n"; return os; }
void Yes(bool b) { cout << (b ? "Yes" : "No") << endl; }
void YES(bool b) { cout << (b ? "YES" : "NO") << endl; }
template<class T> inline bool chmin(T& a,T b) {if(a > b){a = b; return true;} return false;}
template<class T> inline bool chmax(T& a,T b) {if(a < b){a = b; return true;} return false;}
const int inf = 1001001001;
const ll linf = 1001001001001001001;

template<typename T>
class lazy_segtree {
    int n;
    vector<T> val,lazy;
    T identity_merge,identity_update;
    function<T(T,T)> merge;
    // update value for specified times
    function<T(T,T,int)> _update;
    void eval(int k,int l,int r) {
        if(lazy[k] == identity_update) return;
        if(k < n-1) {
            lazy[k*2+1] = _update(lazy[k*2+1],lazy[k],1);
            lazy[k*2+2] = _update(lazy[k*2+2],lazy[k],1);
        }
        val[k] = _update(val[k],lazy[k],r-l);
        lazy[k] = identity_update;
    }

public:
    lazy_segtree(int _n,vector<T> init,T identity_merge,T identity_update,
            function<T(T,T)> merge,function<T(T,T,int)> update)
            :identity_merge(identity_merge),identity_update(identity_update),merge(merge),_update(update) {
        n = 1;
        while(n < _n) n *= 2;
        val = vector<T>(2*n-1,identity_merge);
        lazy = vector<T>(2*n-1,identity_update);
        rep(i,_n) val[i+n-1] = init[i];
        rrep(i,n-1) val[i] = merge(val[i*2+1],val[i*2+2]);
    }
    void update(int a,int b,T x,int k = 0,int l = 0,int r = -1) {
        if(r == -1) r = n;
        eval(k,l,r);
        if(a <= l && r <= b) {
            lazy[k] = _update(lazy[k],x,1);
            eval(k,l,r);
        } else if(a < r && l < b) {
            update(a,b,x,k*2+1,l,(l+r)/2);
            update(a,b,x,k*2+2,(l+r)/2,r);
            val[k] = merge(val[k*2+1],val[k*2+2]);
        }
    }
    // segment [a,b)
    T query(int a,int b,int k = 0,int l = 0,int r = -1) {
        if(r == -1) r = n;
        eval(k,l,r);
        if(b <= l || r <= a) return identity_merge;
        if(a <= l && r <= b) return val[k];
        T t1 = query(a,b,2*k+1,l,(l+r)/2);
        T t2 = query(a,b,2*k+2,(l+r)/2,r);
        return merge(t1,t2);
    }
    pair<T,T> operator[](int i) const { return make_pair(val[i],lazy[i]); }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    int n,q;
    cin >> n >> q;
    auto f = [](int a,int b) {
        return min(a,b);
    };
    auto g = [](int a,int b,int c) {
        return a+b;
    };
    lazy_segtree<int> st(n,vi(n,0),inf,0,f,g);
    rep(_,q) {
        int i;
        cin >> i;
        if(i == 0) {
            int s,t,x;
            cin >> s >> t >> x;
            t++;
            st.update(s,t,x);
        } else {
            int s,t;
            cin >> s >> t;
            t++;
            cout << st.query(s,t) << endl;
        }
    }
}


Measured memory_bytes: 5204