#include <atcoder/all>
#include <cmath>
#include <cstdint>
#include <iostream>
#include <map>

using namespace std;
using namespace atcoder;

using mint = modint998244353;
using i32 = int32_t;

#define REP(i, s, t) for (i32 i = (s); i < (t); ++i)
#define PER(i, s, t) for (i32 i = (t)-1; i >= (s); --i)

vector<mint> fact, ifact, inv;

const i32 m = 100000;

void init(void) {
    fact.resize(m + 1, 1);
    ifact.resize(m + 1, 1);
    inv.resize(m + 1, 1);
    REP(i, 1, m + 1) fact.at(i) = i * fact.at(i - 1);
    ifact.at(m) = fact.at(m).inv();
    PER(i, 1, m) {
        inv.at(i + 1) = ifact.at(i + 1) * fact.at(i);
        ifact.at(i) = ifact.at(i + 1) * (i + 1);
    }
}

i32 read_int(void) {
    i32 n;
    cin >> n;
    return n;
}

int main(void) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    init();
    const i32 k = read_int();
    const i32 q = read_int();
    vector<mint> dp(m + 1);
    dp[0] = 1;
    mint sum = 1;
    REP(i, 1, m + 1) {
        if (i > k) sum -= dp[i - k - 1];
        dp[i] = sum * inv[i];
        sum += dp[i];
    }
    const i32 batch = min(m * sqrt(log(m) / q), (double)m);
    cout << batch << "\n";
    vector<vector<mint>> memo;
    REP(i, 0, m / batch) {
        vector<mint> a(dp.begin(), dp.begin() + i * batch);
        vector<mint> b = convolution(a, dp);
        if (b.empty()) {
            b.resize(m + 1);
        }
        memo.emplace_back(b);
    }
    auto calc = [&](const i32 n, const i32 k) -> mint {
        assert(k <= n);
        if (k < 0) return 0;
        const i32 p = k / batch;
        mint res = memo[p][n];
        REP(i, p * batch, k + 1) res += dp[i] * dp[n - i];
        return res;
    };
    REP(i, 0, q) {
        const i32 n = read_int();
        const i32 l = read_int();
        const i32 r = read_int();
        mint ans = calc(n - 1, r - 1) - calc(n - 1, l - 2);
        ans *= fact[n - 1];
        cout << ans.val() << "\n";
    }
    return 0;
}