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

#ifdef DEBUG
#include "debug.h"
#else
#include "dzilib.h"
#define debug(...) 42
#endif

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define repp(i, n, m) for (int i = (n); i < (m); ++i)

#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)
#define reppr(i, n, m) for (int i = (m) - 1; i >= (n); --i)

#define each(a,x) for(auto& a : (x))
#define sz(x) int((x).size())

using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using pi = pair<int, int>;
using pll = pair<ll, ll>;

template <typename T, typename V> void mini(T& a, V b) {if (b < a) a = b; }
template <typename T, typename V> void maxi(T& a, V b) {if (b > a) a = b; }

typedef unsigned long long ull;
ull modmul(ull a, ull b, ull M) {
ll ret = a * b - M * ull(1.L / M * a * b);
return ret + M * (ret < 0) - M * (ret >= (ll)M);
}
ull modpow(ull b, ull e, ull mod) {
ull ans = 1;
for (; e; b = modmul(b, b, mod), e /= 2)
if (e & 1) ans = modmul(ans, b, mod);
return ans;
}
bool isPrime(ull n) {
if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
s = __builtin_ctzll(n-1), d = n >> s;
for (ull a : A) { // ^ count t r a i l i n g zeroes
ull p = modpow(a%n, d, n), i = s;
while (p != 1 && p != n - 1 && a % n && i--)
p = modmul(p, p, n);
if (p != n-1 && i != s) return 0;
}
return 1;
}
ull pollard(ull n) {
auto f = [n](ull x) { return modmul(x, x, n) + 1; };
ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
while (t++ % 40 || __gcd(prd, n) == 1) {
if (x == y) x = ++i, y = f(x);
if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
x = f(x), y = f(f(y));
}
return __gcd(prd, n);
}
vector<ull> factor(ull n) {
if (n == 1) return {};
if (isPrime(n)) return {n};
ull x = pollard(n);
auto l = factor(x), r = factor(n / x);
l.insert(l.end(), all(r));
return l;
}
int tau(ll x) {
    // debug(x);
    int r = 1;
    auto process = [&](ull p) {
        int v = 0;
        while (x % p == 0) {
            x /= p;
            ++v;
        }
        r *= v + 1;
    };
    process(2);
    process(3);
    for (ull p : factor(x))
        process(p);
    return r;
}

#ifdef DEBUG
namespace hidden {
int T, Q, count = 0;
ll N, C;
vll xs = []() -> vll {
    cin >> T >> N >> Q >> C;
    vll xlist(T);
    for (auto &a : xlist)
        cin >> a;
    return {rall(xlist)};
}();
}
// Spytaj o T - liczbę przypadków testowych.
int GetT() { return hidden::T; }
// Spytaj o N - ograniczenie na x.
long long GetN() { return hidden::N; }
// Spytaj o Q - limit na liczbę zadanych zapytań.
int GetQ() { return hidden::Q; }
// Spytaj o C - ograniczenie na y.
long long GetC() { return hidden::C; }
// Spytaj o liczbę dzielników liczby x+y.
long long Ask(long long y) {
    assert(++hidden::count <= hidden::Q && y <= hidden::C);
    return tau(hidden::xs.back() + y);
}
// Udziel odpowiedzi.
void Answer(long long z) {
    assert(z == hidden::xs.back());
    hidden::xs.pop_back();
}
#endif

map<ll, int> asked;
int ask(ll x) {
    if (!asked.count(x))
        asked[x] = Ask(x);
    return asked[x];
}
bool verify(ll x) {
    for (auto [q, ans] : asked)
        if (tau(q + x) != ans)
            return false;
    return true;
}

const ll INF = 1e18;
mt19937_64 rnd(263448562);
array<array<ll, 60>, 60> powers;
array<int, 240> v2s, v3s;

void solvetc(ll N, int Q, ll C) {
    assert(C && Q);
    ll add = rnd() % N + N / 3;
    int v2 = 0, v3 = 0;

    array<array<int, 3>, 2> chineese{};
    rep(i, 6)
        chineese[i % 2][i % 3] = i;

    while (powers[v2][v3] * 5000 < N) {
        vi taus;
        auto psh = [&]() { taus.push_back(ask(add + powers[v2][v3] * sz(taus))); };
        psh(); psh(); psh();

        array<int, 6> can{};
        while (true) {
            fill(all(can), 0);

            rep(m2, sz(taus)) rep(m3, sz(taus)) {
                bool ok = false;
                repp(nv2, v2 + 1, sz(powers)) repp(nv3, v3 + 1, sz(powers[0])) {
                    if (powers[nv2][nv3] == INF)
                        break;
                    if (2 * powers[nv2 - v2][0] <= sz(taus))
                        continue;
                    if (3 * powers[0][nv3 - v3] <= sz(taus))
                        continue;
                    // debug(nv2, nv3, m2, m3);
                    if (m2 == m3) {
                        if (taus[m2] % ((nv2 + 1) * (nv3 + 1)))
                            continue;
                    }
                    else {
                        if (taus[m2] % ((nv2 + 1) * (v3s[abs(m2 - m3)] + 1 + v3)))
                            continue;
                        if (taus[m3] % ((nv3 + 1) * (v2s[abs(m2 - m3)] + 1 + v2)))
                            continue;
                    }
                    bool skip = false;

                    rep(i, sz(taus)) if (i != m2 && i != m3)
                        if (taus[i] % ((v2s[abs(i - m2)] + 1 + v2) * (v3s[abs(i - m3)] + 1 + v3)))
                            skip = true;

                    if (!skip)
                        ok = true;
                }
                if (ok)
                    can[chineese[m2 % 2][m3 % 3]] = true;
            }
            // debug(taus, can);
            int acc = accumulate(all(can), 0);
            assert(acc >= 1);
            if (acc == 1)
                break;
            psh();
        }
        // debug(taus, can);
        int id = 0;
        while (!can[id])
            ++id;
        add += id * powers[v2][v3];
        ++v2; ++v3;
    }

    // debug(sz(asked), powers[v2][v3]);

    add = ((-add) % powers[v2][v3] + powers[v2][v3]) % powers[v2][v3];

    // debug(add, powers[v2][v3]);

    while (!verify(add))
        add += powers[v2][v3];
    // debug(add);
    Answer(add);
}

void solve() {
    rep(i, sz(powers)) rep(j, sz(powers[0])) {
        powers[i][j] = 1;
        if (i) powers[i][j] = 2 * powers[i-1][j];
        if (j) powers[i][j] = 3 * powers[i][j-1];
        mini(powers[i][j], INF);
    }
    repp(i, 1, sz(v2s)) if (i % 2 == 0)
        v2s[i] = 1 + v2s[i / 2];
    repp(i, 1, sz(v3s)) if (i % 3 == 0)
        v3s[i] = 1 + v3s[i / 3];

    int T = GetT(), Q = GetQ();
    ll N = GetN(), C = GetC();
    while (T--) {
        asked.clear();
        solvetc(N, Q, C);
    }
    debug(hidden::count);
}

int main() {
#ifdef DEBUG
    const int MEMSIZE = 1024 * 1024 * 1024;
    static_assert(MEMSIZE % 16 == 0);
    static char stack[MEMSIZE];
    asm volatile (
        "mov %[newstack], %%rsp\n"
        "call *%[funcptr]"
        :: [funcptr] "r" (solve), [newstack] "r" (stack + MEMSIZE)
    );
    exit(0);
#else
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    solve();
#endif
}