#include <bits/stdc++.h>
using namespace std;

template <typename Monoid, typename OperatorMonoid = Monoid>
struct LazySegmentTree
{
    using F = function<Monoid(Monoid, Monoid)>;
    using G = function<Monoid(Monoid, OperatorMonoid)>;
    using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;

    int sz, height;
    vector<Monoid> data;
    vector<OperatorMonoid> lazy;
    const F f;
    const G g;
    const H h;
    const Monoid M1;
    const OperatorMonoid OM0;

    LazySegmentTree(int n, const F f, const G g, const H h,
                    const Monoid &M1, const OperatorMonoid OM0)
        : f(f), g(g), h(h), M1(M1), OM0(OM0)
    {
        sz = 1;
        height = 0;
        while (sz < n)
            sz <<= 1, height++;
        data.assign(2 * sz, M1);
        lazy.assign(2 * sz, OM0);
    }

    void set(int k, const Monoid &x)
    {
        data[k + sz] = x;
    }

    void build()
    {
        for (int k = sz - 1; k > 0; k--)
        {
            data[k] = f(data[2 * k + 0], data[2 * k + 1]);
        }
    }

    inline void propagate(int k)
    {
        if (lazy[k] != OM0)
        {
            lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
            lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
            data[k] = reflect(k);
            lazy[k] = OM0;
        }
    }

    inline Monoid reflect(int k)
    {
        return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
    }

    inline void recalc(int k)
    {
        while (k >>= 1)
            data[k] = f(reflect(2 * k + 0), reflect(2 * k + 1));
    }

    inline void thrust(int k)
    {
        for (int i = height; i > 0; i--)
            propagate(k >> i);
    }

    void update(int a, int b, const OperatorMonoid &x)
    {
        thrust(a += sz);
        thrust(b += sz - 1);
        for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1)
        {
            if (l & 1)
                lazy[l] = h(lazy[l], x), ++l;
            if (r & 1)
                --r, lazy[r] = h(lazy[r], x);
        }
        recalc(a);
        recalc(b);
    }

    Monoid query(int a, int b)
    {
        thrust(a += sz);
        thrust(b += sz - 1);
        Monoid L = M1, R = M1;
        for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1)
        {
            if (l & 1)
                L = f(L, reflect(l++));
            if (r & 1)
                R = f(reflect(--r), R);
        }
        return f(L, R);
    }

    Monoid operator[](const int &k)
    {
        return query(k, k + 1);
    }

    template <typename C>
    int find_subtree(int a, const C &check, Monoid &M, bool type)
    {
        while (a < sz)
        {
            propagate(a);
            Monoid nxt = type ? f(reflect(2 * a + type), M) : f(M, reflect(2 * a + type));
            if (check(nxt))
                a = 2 * a + type;
            else
                M = nxt, a = 2 * a + 1 - type;
        }
        return a - sz;
    }

    template <typename C>
    int find_first(int a, const C &check)
    {
        Monoid L = M1;
        if (a <= 0)
        {
            if (check(f(L, reflect(1))))
                return find_subtree(1, check, L, false);
            return -1;
        }
        thrust(a + sz);
        int b = sz;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1)
        {
            if (a & 1)
            {
                Monoid nxt = f(L, reflect(a));
                if (check(nxt))
                    return find_subtree(a, check, L, false);
                L = nxt;
                ++a;
            }
        }
        return -1;
    }

    template <typename C>
    int find_last(int b, const C &check)
    {
        Monoid R = M1;
        if (b >= sz)
        {
            if (check(f(reflect(1), R)))
                return find_subtree(1, check, R, true);
            return -1;
        }
        thrust(b + sz - 1);
        int a = sz;
        for (b += sz; a < b; a >>= 1, b >>= 1)
        {
            if (b & 1)
            {
                Monoid nxt = f(reflect(--b), R);
                if (check(nxt))
                    return find_subtree(b, check, R, true);
                R = nxt;
            }
        }
        return -1;
    }
};
long long f(long long a, long long b)
{
    return min(a,b);
}
long long g(long long a, long long b)
{
    return a + b;
}
long long h(long long a, long long b)
{
    return a + b;
}

int main()
{
    int n, q;
    cin >> n >> q;
    LazySegmentTree<long long> lsg(n + 10, f, g, h, 1e18, 0);
    for(int i = 0;i<=n;i++){
        lsg.set(i,0);
    }
    lsg.build();
    for (int i = 0; i < q; i++)
    {
        int type;
        cin >> type;
        if (type == 0)
        {
            int s, t, x;
            cin >> s >> t >> x;
            lsg.update(s, t+1, x);
        }
        else
        {
            int s, t;
            cin >> s >> t;
            cout << lsg.query(s, t+1)<<endl;
        }
    }
}


Measured memory_bytes: 7032