#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //Integer-Related typedef long long i64; typedef unsigned long long ui64; //vector-Related template using vv = vector>; template using vvv = vector>>; typedef vector vi64; typedef vector vbool; typedef vv vvi64; typedef vv vvbool; typedef vvv vvvi64; typedef vvv vvvbool; typedef pair pi64; typedef vector vstr; //これで最大値優先 template> using prque = priority_queue, Pred>; //set-Related #include typedef set si64; typedef multiset msi64; typedef unordered_set usi64; //Calculation-Related inline i64 rm(const i64 l, const i64 r) { i64 val = l % r; if (val >= 0) { return val; } else { return val + r; } } template T r_accumulate(const vector& vec) { return std::accumulate(vec.begin(), vec.end(), T{}); } template void r_insert(vector& to, vector& from) { ranges::copy(from, back_inserter(to)); } constexpr std::string repeater3030(const std::string& s, int number) { std::string cur = ""; for (i64 i = 0; i < number; i++) { cur += s; } return cur; } constexpr std::string repeater3030(const char& c, int number) { string s(1, c); return repeater3030(s, number); } constexpr i64 pow_i64(i64 base, i64 exp) { i64 res = 1LL; while (exp > 0LL) { if (exp & 1) { res *= base; } exp >>= 1LL; base *= base; } return res; } template T eqmin(T& a, T b) { a = min(a, b); return a; } template T eqmax(T& a, T b) { a = max(a, b); return a; } //Output-Related template std::ostream& operator<<(std::ostream& os, const std::pair& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } template inline void output(const T elem) { std::cout << elem << std::endl; } #ifndef __INTELLISENSE__ template inline void output(const pair elem) { std::cout << "(" << elem.first << "," << elem.second << ")" << std::endl; } template inline void output(const vector& vec) { for (T elem : vec) { std::cout << elem << " "; } std::cout << std::endl; } template inline void output(const vector>& vvec) { for (vector vec : vvec) { std::cout << "("; for (T elem : vec) { std::cout << elem << " "; } std::cout << ")"; } std::cout << std::endl; } template inline void output(const vector>>& vvvec) { for (vector> vvec : vvvec) { std::cout << "["; for (vector vec : vvec) { std::cout << "("; for (T elem : vec) { std::cout << elem << " "; } std::cout << ")"; } std::cout << "]" << std::endl; } } #endif template inline void output_iter(const T& iter) { for (auto&& elem : iter) { std::cout << elem << " "; } std::cout << std::endl; } /** * ACLibrary-fewnwicktree * Ref : https://atcoder.github.io/ac-library/master/document_ja/ */ /** * ACLibrary-internaltypetraits * Ref : https://atcoder.github.io/ac-library/master/document_ja/ */ #include namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder namespace atcoder { // Reference: https://en.wikipedia.org/wiki/Fenwick_tree template struct fenwick_tree { using U = internal::to_unsigned_t; public: fenwick_tree() : _n(0) {} explicit fenwick_tree(int n) : _n(n), data(n) {} void add(int p, T x) { assert(0 <= p && p < _n); p++; while (p <= _n) { data[p - 1] += U(x); p += p & -p; } } T sum(int l, int r) { assert(0 <= l && l <= r && r <= _n); return sum(r) - sum(l); } private: int _n; std::vector data; U sum(int r) { U s = 0; while (r > 0) { s += data[r - 1]; r -= r & -r; } return s; } }; } // namespace atcoder /** * ACLibrary-segtree * Ref : https://atcoder.github.io/ac-library/master/document_ja/ */ /** * ACLibrary-internalbit * Ref : https://atcoder.github.io/ac-library/master/document_ja/ */ #ifdef _MSC_VER #include #endif #if __cplusplus >= 202002L #endif namespace atcoder { namespace internal { #if __cplusplus >= 202002L using std::bit_ceil; #else // @return same with std::bit::bit_ceil unsigned int bit_ceil(unsigned int n) { unsigned int x = 1; while (x < (unsigned int)(n)) x *= 2; return x; } #endif // @param n `1 <= n` // @return same with std::bit::countr_zero int countr_zero(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } // @param n `1 <= n` // @return same with std::bit::countr_zero constexpr int countr_zero_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } } // namespace internal } // namespace atcoder namespace atcoder { #if __cplusplus >= 201703L template struct segtree { static_assert(std::is_convertible_v>, "op must work as S(S, S)"); static_assert(std::is_convertible_v>, "e must work as S()"); #else template struct segtree { #endif public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {} explicit segtree(const std::vector& v) : _n(int(v.size())) { size = (int)internal::bit_ceil((unsigned int)(_n)); log = internal::countr_zero((unsigned int)size); d = std::vector(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return d[1]; } template int max_right(int l) const { return max_right(l, [](S x) { return f(x); }); } template int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r) const { return min_left(r, [](S x) { return f(x); }); } template int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } // namespace atcoder using namespace atcoder; /** * Graph一式 * Author : WhiteKnight */ struct Dest { i64 to; i64 cost; }; typedef vector> wgraphList;//Weighted,List typedef vector> sgraphList;//Simple,List typedef vector vedge; typedef vvi64 wgraphMat;//Weighted,Matrix wgraphList translate_simple_weight(sgraphList graph) { i64 N = graph.size(); wgraphList res(N); for (i64 i = 0; i < N; i++) { for (auto&& e : graph[i]) { res[i].push_back({e,1}); } } return res; } //コストを無視し構造のみのグラフを返す sgraphList translate_weight_simple(wgraphList graph){ i64 N = graph.size(); sgraphList res(N); for (i64 i = 0; i < N; i++) { for (auto&& e : graph[i]) { res[i].push_back(e.to); } } return res; } template wgraphList translate_mat_list(wgraphMat graph){ i64 N = graph.size(); wgraphList res(N); for (i64 i = 0; i < N; i++) { for (i64 j = 0; j < N; j++) { if(graph[i][j] >= INF){ continue; } res[i].push_back({ j,graph[i][j] }); } } return res; } /** * ACLibrary-math * Ref : https://atcoder.github.io/ac-library/master/document_ja/ */ /** * ACLibrary-internalmath * Ref : https://atcoder.github.io/ac-library/master/document_ja/ */ #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned long long y = x * _m; return (unsigned int)(z - y + (z < y ? _m : 0)); } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder namespace atcoder { long long pow_mod(long long x, long long n, int m) { assert(0 <= n && 1 <= m); if (m == 1) return 0; internal::barrett bt((unsigned int)(m)); unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m)); while (n) { if (n & 1) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 1; } return r; } long long inv_mod(long long x, long long m) { assert(1 <= m); auto z = internal::inv_gcd(x, m); assert(z.first == 1); return z.second; } // (rem, mod) std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) long long g, im; std::tie(g, im) = internal::inv_gcd(m0, m1); long long u1 = (m1 / g); // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if ((r1 - r0) % g) return {0, 0}; // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) long long x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } long long floor_sum(long long n, long long m, long long a, long long b) { assert(0 <= n && n < (1LL << 32)); assert(1 <= m && m < (1LL << 32)); unsigned long long ans = 0; if (a < 0) { unsigned long long a2 = internal::safe_mod(a, m); ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m); a = a2; } if (b < 0) { unsigned long long b2 = internal::safe_mod(b, m); ans -= 1ULL * n * ((b2 - b) / m); b = b2; } return ans + internal::floor_sum_unsigned(n, m, a, b); } } // namespace atcoder //Main Flow int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << setprecision(15); i64 T; cin >> T; for (i64 testCase = 0; testCase < T; testCase++) { i64 M; cin >> M; i64 ldigits = 0; for (i64 i = 1; i < 10; i++) { i64 d; cin >> d; for (i64 j = 0; j < d; j++) { ldigits *= 10; ldigits += i; } } vi64 r = { ldigits,0 }; vi64 m = { pow_i64(10,9),M }; auto res = crt(r,m); output(res.first); } return 0; }