/* Problem URL: https://codeforces.com/edu/course/2/lesson/7/2/practice/contest/289391/problem/I */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;

    vi dsu(n);
    rep(i, n) {
        dsu[i] = i;
    }

    vi depth(n);

    function<pair<int, int>(int)> find_p = [&](int i) -> pair<int, int>{
        if (dsu[i] == i) {
            return {i, 0};
        }

        auto ans = find_p(dsu[i]);
        dsu[i] = ans.first;
        depth[i] ^= ans.second;

        return {dsu[i], depth[i]};
    };

    auto join = [&](int a, int b) {
        auto ap = find_p(a);
        auto bp = find_p(b);

        dsu[bp.first] = ap.first;
        depth[bp.first] = (1 ^ bp.second ^ ap.second);
    };
    
    int shift = 0;
    function<void(int, int)> func[] = {
        [&](int a, int b) {
            join(a, b);
        },
        [&](int a, int b) {
            find_p(a);
            find_p(b);

            int ca = depth[a];
            int cb = depth[b];

            if (ca == cb) {
                cout << "YES\n";
                shift++;
                return;
            }

            cout << "NO\n";
        }
    };

    while (m--) {
        int op, a, b;
        cin >> op >> a >> b;
        a = (a + shift) % n;
        b = (b + shift) % n;
        func[op](a, b);
    }
}