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

#include "testlib.h"

using namespace std;
using namespace atcoder;

using mint = modint998244353;
using i32 = int32_t;
using u64 = uint64_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);
    }
}

int main(int argc, char **argv) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    registerValidation(argc, argv);
    init();
    const i32 k = inf.readInt(1, m);
    inf.readSpace();
    const i32 q = inf.readInt(1, m);
    inf.readEoln();

    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];
    }
    auto ep = convolution(dp, dp);
    REP(i, 0, q) {
        const i32 n = inf.readInt(1, m);
        inf.readSpace();
        const i32 l = inf.readInt(1, n);
        inf.readSpace();
        const i32 r = inf.readInt(l, n);
        inf.readEoln();

        const u64 q = numeric_limits<u64>::max() - (u64)998244352 * 998244352;
        const u64 sub = q / 998244353 * 998244353;

        u64 sum = 0;
        REP(i, l, r + 1) {
            sum += (u64)dp[i - 1].val() * dp[n - i].val();
            if (sum >= q) {
                sum -= sub;
            }
        }
        mint ans = sum;
        ans *= fact[n - 1];
        cout << ans.val() << "\n";
    }
    inf.readEof();
    return 0;
}