#include <algorithm>
#include <limits>
#include <iostream>
#include <type_traits>
#include <vector>
#include <cstdint>
#include <cassert>
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/all/DSL_2_H"
template<typename Element>
struct plus
{
    using element_type  = Element;
    using operator_type = element_type;
    plus()              = delete;
    static operator_type compose(const operator_type& a, const operator_type& b) { return a + b; }
    static constexpr operator_type id() { return operator_type{}; }
};

constexpr unsigned int mod                  = 1000000007;
template<typename T> constexpr T inf_v      = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
template<typename Element>
struct min
{
    using element_type = Element;
    using value_type   = element_type;
    min()              = delete;
    static value_type merge(const value_type& a, const value_type& b) { return std::min(a, b); }
    static constexpr value_type id() { return inf_v<value_type>; }
};
template<typename ValueElement, typename OperatorElement>
struct min_plus
{
    using value_element_type    = ValueElement;
    using operator_element_type = OperatorElement;
    using value_monoid_type     = min<value_element_type>;
    using operator_monoid_type  = plus<operator_element_type>;
    using value_type            = typename value_monoid_type::value_type;
    using operator_type         = typename operator_monoid_type::operator_type;
    min_plus()                  = delete;
    template<typename Ind>
    static value_type apply(const operator_type& f, const value_type& x, const Ind) { return std::min(static_cast<value_type>(f) + x, value_monoid_type::id()); }
};

using i32   = int32_t;
using i64   = int64_t;
using u32   = uint32_t;
using u64   = uint64_t;
using uint  = unsigned int;
using usize = std::size_t;
using ll    = long long;
using ull   = unsigned long long;
using ld    = long double;
template<typename T, usize n>
using arr = T (&)[n];
template<typename T, usize n>
using c_arr = const T (&)[n];
template<typename T>
T in()
{
    T v;
    return std::cin >> v, v;
}
template<typename T, typename Uint, usize n, usize i>
T in_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type) { return in<T>(); }
template<typename T, typename Uint, usize n, usize i>
auto in_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type& szs)
{
    const usize s = (usize)szs[i];
    std::vector<decltype(in_v<T, Uint, n, i + 1>(szs))> ans(s);
    for (usize j = 0; j < s; j++) { ans[j] = in_v<T, Uint, n, i + 1>(szs); }
    return ans;
}
template<typename T, typename Uint, usize n>
auto in_v(c_arr<Uint, n> szs) { return in_v<T, Uint, n, 0>(szs); }
template<typename... Types>
auto in_t() { return std::tuple<std::decay_t<Types>...>{in<Types>()...}; }

template<typename T>
void out(const T& v) { std::cout << v; }
template<typename T>
void out(const std::vector<T>& v)
{
    for (usize i = 0; i < v.size(); i++) {
        if (i > 0) { std::cout << ' '; }
        out(v[i]);
    }
    std::cout << "\n";
}
template<typename T1, typename T2>
void out(const std::pair<T1, T2>& v) { out(v.first), std::cout << ' ', out(v.second); }
template<typename T, typename... Args>
void out(const T& v, const Args... args) { out(v), std::cout << ' ', out(args...); }
template<typename... Args>
void outln(const Args... args) { out(args...), std::cout << '\n'; }
template<typename... Args>
void outel(const Args... args) { out(args...), std::cout << std::endl; }

template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename MonoidAct>
class lazyseg
{
public:
    using monoid_act_type      = MonoidAct;
    using value_monoid_type    = typename monoid_act_type::value_monoid_type;
    using operator_monoid_type = typename monoid_act_type::operator_monoid_type;
    using value_type           = typename value_monoid_type::value_type;
    using operator_type        = typename operator_monoid_type::operator_type;
    lazyseg(const usize sz, const value_type initial = value_monoid_type::id()) : sz{sz}, depth{clog(sz)}, half{static_cast<usize>(1) << depth}, val(half << 1, value_monoid_type::id()), op(half << 1, operator_monoid_type::id())
    {
        if (initial != value_monoid_type::id()) {
            std::fill(val.begin() + half, val.end(), initial);
            for (usize i = half - 1; i >= 1; i--) { up(i); }
        }
    }
    template<typename InIt>
    lazyseg(const InIt first, const InIt last) : sz{static_cast<usize>(std::distance(first, last))}, depth{clog(sz)}, half{static_cast<usize>(1) << depth}, val(half << 1, value_monoid_type::id()), op(half << 1, operator_monoid_type::id())
    {
        std::copy(first, last, val.begin() + half);
        for (usize i = half - 1; i >= 1; i--) { up(i); }
    }
    value_type get(const usize a) { return assert(a < sz), fold(a, a + 1); }
    void set(usize a, const value_type& v)
    {
        assert(a < sz);
        top_down(a += half), top_down(a + 1), op[a] = operator_monoid_type::id(), val[a] = v;
        while (a >>= 1) { up(a); }
    }
    value_type fold(usize l, usize r)
    {
        assert(l < r), assert(r <= sz);
        top_down(l += half), top_down(r += half);
        value_type accl = value_monoid_type::id(), accr = value_monoid_type::id();
        for (; l < r; l >>= 1, r >>= 1) {
            if (l & 1) { accl = value_monoid_type::merge(accl, val[l++]); }
            if (r & 1) { accr = value_monoid_type::merge(val[--r], accr); }
        }
        return value_monoid_type::merge(accl, accr);
    }
    void act(usize l, usize r, const operator_type& f)
    {
        assert(l < r), assert(r <= sz);
        const usize lin = l + half, rin = r + half;
        top_down(l += half), top_down(r += half);
        for (usize ls = 1, rs = 1; l < r; l >>= 1, r >>= 1, ls <<= 1, rs <<= 1) {
            if (l & 1) { update(l++, f, ls); }
            if (r & 1) { update(--r, f, rs); }
        }
        bottom_up(lin), bottom_up(rin);
    }
    usize size() const { return sz; }
    friend std::ostream& operator<<(std::ostream& os, const lazyseg& lseg)
    {
        auto lseg2 = lseg;
        os << "[";
        for (usize i = 0; i < lseg.sz; i++) { os << lseg2.get(i) << (i + 1 == lseg2.sz ? "" : ","); }
        return (os << "]\n");
    }

private:
    void up(const usize i) { val[i] = value_monoid_type::merge(val[i << 1], val[i << 1 | 1]); }
    void update(const usize a, const operator_type& f, const usize l) { op[a] = operator_monoid_type::compose(f, op[a]), val[a] = monoid_act_type::apply(f, val[a], l); }
    void down(const usize a, const usize l) { update(a << 1, op[a], l >> 1), update(a << 1 | 1, op[a], l >> 1), op[a] = operator_monoid_type::id(); }
    void top_down(const usize a)
    {
        const usize b = (a / (a & -a)) >> 1;
        for (usize i = 0, l = half; i < depth; i++, l >>= 1) {
            const usize v = a >> (depth - i);
            if (v > b) { break; }
            down(v, l);
        }
    }
    void bottom_up(usize a)
    {
        a = (a / (a & -a)) >> 1;
        for (; a >= 1; a >>= 1) { up(a); }
    }
    const usize sz, depth, half;
    std::vector<value_type> val;
    std::vector<operator_type> op;
};
int main()
{
    const auto n = in<usize>();
    const auto q = in<usize>();
    lazyseg<min_plus<ll, ll>> seg(n, 0LL);
    for (usize i = 0; i < q; i++) {
        const auto c = in<usize>();
        if (c == 0) {
            const auto l = in<usize>();
            const auto r = in<usize>() + 1;
            const auto x = in<ll>();
            seg.act(l, r, x);
        } else {
            const auto l = in<usize>();
            const auto r = in<usize>() + 1;
            outln(seg.fold(l, r));
        }
    }
    return 0;
}



Measured memory_bytes: 7068