#pragma GCC optimize ("O3") #pragma GCC target ("avx") #include using namespace std; #ifndef LOCAL #define getchar getchar_unlocked #define putchar putchar_unlocked #endif int in() { int n, c; while ((c = getchar()) < '0') if (c == EOF) abort(); n = c - '0'; while ((c = getchar()) >= '0') n = n * 10 + c - '0'; return n; } void out(int n) { int res[11], i = 0; do { res[i++] = n % 10, n /= 10; } while (n); while (i) putchar(res[--i] + '0'); putchar('\n'); } int p2[6], inv[9]; int count(int n) { int res = 0; while (n % 3 == 0) n /= 3, res++; return res; } pair decomp(int n) { if (n == 0) return{ 0, 0 }; int three = 0; while (n % 3 == 0) { n /= 3; three++; } return{ inv[n % 9], three }; } int main() { p2[0] = 1; for (int i = 1; i < 6; i++) p2[i] = p2[i - 1] * 2 % 9; for (int i = 0; i < 6; i++) inv[p2[i]] = i; int T = in(); while (T--) { int n = in() - 1, x = in(), a = in(), b = in(), m = in(); auto N = decomp(n); pair L(0, 0); pair R = N; bool zero = true; int64_t ans = 0; for (int i = 0; i <= n; i++) { if (x % 10 != 0) zero = false; int two = (N.first - L.first - R.first) % 6; int three = N.second - L.second - R.second; int c = p2[two] * (three == 0 ? 1 : three == 1 ? 3 : 0); ans += c * (x % 10); auto ll = decomp(i + 1); auto rr = decomp(n - i); L.first += ll.first; L.second += ll.second; R.first -= rr.first; R.second -= rr.second; x = ((x ^ a) + b) % m; } ans %= 9; if (ans == 0) ans = 9; if (zero) ans = 0; out(ans); } }