#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template static void amin(T &x, U y) { if(y < x) x = y; } template static void amax(T &x, U y) { if(x < y) x = y; } struct BinCoeffPrimePower { enum { p = 3, q = 2, P = 9 }; typedef uint8_t Num; vector fact; //(x!)_p vector factinv; //fact[x]^{-1} mod P vector prodfact; Num invTable[P]; vector digitsum; void init(int maxN_) { int maxN = min(max(0, maxN_), P - 1); fact.resize(maxN + 1); fact[0] = 1; for(int x = 1; x <= maxN; ++ x) { fact[x] = x % p == 0 ? fact[x - 1] : mul(fact[x - 1], x); } factinv.resize(maxN + 1); factinv[maxN] = inverse(fact[maxN]); for(int x = maxN; x >= 1; -- x) { factinv[x - 1] = x % p == 0 ? factinv[x] : mul(factinv[x], x); } } void precomputeAll(int N) { prodfact.resize(N + 1); prodfact[0] = 1; for(int n = 1; n <= N; ++ n) prodfact[n] = mul(prodfact[n / p], fact[n % P]); for(int n = 1; n < P; ++ n) invTable[n] = inverse(n); int N_p = N / p; digitsum.resize(N_p + 1); digitsum[0] = 0; for(int n = 1; n <= N_p; ++ n) digitsum[n] = n + digitsum[n / p]; } int getP() const { return P; } Num nCr(int n, int r) const { if(r > n) return 0; assert(0 <= n && (n >= getP() || n < (int)fact.size()) && 0 <= r); int z = n - r; int e0 = 0; e0 += digitsum[n / p]; e0 -= digitsum[r / p]; e0 -= digitsum[z / p]; int em = 0; em += digitsum[n / P]; em -= digitsum[r / P]; em -= digitsum[z / P]; Num prod = 1; prod = mul(prod, prodfact[n]); prod = mul(prod, invTable[prodfact[r]]); prod = mul(prod, invTable[prodfact[z]]); if(!(p == 2 && q >= 3) && em % 2 != 0) prod = P - prod; for(int i = 0; i < e0 && i < q; ++ i) prod = mul(prod, p); return prod; } private: Num mul(Num x, Num y) const { return x * y % P; } int inverse(signed a) const { a %= P; if(a < 0) a += P; signed b = P, u = 1, v = 0; while(b) { signed t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0) u += P; return u; } }; int main() { BinCoeffPrimePower bc; bc.init(10000000); bc.precomputeAll(10000000); int T; scanf("%d", &T); for(int ii = 0; ii < T; ++ ii) { int n; scanf("%d", &n); int x; int a; int b; int m; scanf("%d%d%d%d", &x, &a, &b, &m); int ans = 0; bool allzero = true; for(int r = x, i = 0; i < n; ++ i) { int S = r % 10; allzero &= S == 0; ans += bc.nCr(n - 1, i) * S; r = ((r ^ a) + b) % m; } ans %= 9; if(!allzero && ans == 0) ans = 9; printf("%d\n", ans); } return 0; }