結果
| 問題 | No.219 巨大数の概算 |
| ユーザー |
 kopricky
|
| 提出日時 | 2018-10-07 09:38:34 |
| 言語 | C++11 (gcc 11.4.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 34,138 bytes |
| コンパイル時間 | 3,163 ms |
| コンパイル使用メモリ | 178,000 KB |
| 実行使用メモリ | 14,724 KB |
| 最終ジャッジ日時 | 2023-08-02 17:59:22 |
| 合計ジャッジ時間 | 9,263 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge11 |
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
ソースコード
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
using namespace std;
const int MAX_N = 100005;
// シフト演算子を使ったり, ビット演算をしたりしていなければ int や long long と同じように動くはず
// 宣言は MPI_(数字 or string) もしくは MPI_ hoge = 数字; またデフォルトは0初期化されます
// 引数の string は 0 を除いて leading-zero がないことを仮定しています
// シフト演算子, および ビット演算(&,|,^) はフォローしていません
// 数字(intやlong long) との演算や比較は暗黙的に MPI_ にキャストされます
// 任意精度の多倍長整数の足し算, 引き算, 掛け算, 割り算(商と余り), 2で割る(div2), sqrt, log10, pow, 絶対値, 大小判定, 入出力, 任意の桁へのランダムアクセス などを行えます
// 2で割る, sqrt, log10 は lower_bound を返します(MPI_型)
// n 桁(10進数)の数に対して 足し算, 引き算(O(n)), 掛け算(O(nlogn)), 割り算(O(n^2)), 2で割る(O(n)), sqrt((10~20)*O(n^2)), log10(O(1)), pow(nlognlogm) の計算時間がかかります
// 掛け算の演算を効率的に行うために本実装では base を 10 にとっています(足し算, 引き算, 割り算を定数倍高速化したいなら base を 10^9 とか 10^18 とかでとったほうがよい)
// 掛け算は NTT を用いています
// 負の除算もフォローしています(定義はC++の除算と同じです)
// 2で割るのは多倍長整数での2分探索やsqrt計算に使う目的で実装しました
// to_ll, to_string で long long, string に変換可能
// 10倍や10で割るなどもO(1)で行うようにできる
class MPI_ : public vector<int> {
private:
static constexpr int root = 5;
static constexpr int MOD_ = 924844033;
static void trim_sign(MPI_& num){
if(num.isZero()) num.sign = false;
}
static void trim_digit(MPI_& num){
while(num.back() == 0 && (int)num.size() >= 2) num.pop_back();
}
static bool abs_less(const MPI_& a, const MPI_& b){
if(a.size() != b.size()) return a.size() < b.size();
for(int index = (int)a.size() - 1; index >= 0; index--){
if(a[index] != b[index]) return a[index] < b[index];
}
return false;
}
static void num_sbst(MPI_& a, const MPI_& b){
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
static void add(const MPI_& a, const MPI_& b, MPI_& res){
num_sbst(res, a);
int mx = (int)max(a.size(), b.size());
res.resize(mx, 0);
int carry = 0;
for(int i = 0; i < mx; i++){
int val = res[i] + ((i < (int)b.size()) ? b[i] : 0) + carry;
carry = val/10;
res[i] = val%10;
}
if(carry) res.push_back(1);
}
static void sub(const MPI_& a, const MPI_& b, MPI_& res){
num_sbst(res, a);
int carry = 0;
for(int i = 0; i < (int)res.size(); i++){
int val = res[i] - carry - ((i < (int)b.size()) ? b[i] : 0);
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
trim_digit(res), trim_sign(res);
}
static int add_(const int x, const int y) { return (x + y < MOD_) ? x + y : x + y - MOD_; }
static int mul_(const int x, const int y) { return (ll)x * y % MOD_; }
static int power(int x, int n){
int res = 1;
while(n > 0){
if(n & 1) res = mul_(res, x);
x = mul_(x, x);
n >>= 1;
}
return res;
}
static int inverse(const int x) { return power(x, MOD_ - 2); }
static void ntt(vector<int>& a, const bool rev = false){
int i,j,k,s,t,v,w,wn;
const int size = (int)a.size();
const int height = (int)log2(2 * size - 1);
for(i = 0; i < size; i++){
j = 0;
for(k = 0; k < height; k++) j |= (i >> k & 1) << (height - 1 - k);
if(i < j) std::swap(a[i], a[j]);
}
for(i = 1; i < size; i *= 2) {
w = power(root, (MOD_ - 1) / (i * 2));
if(rev) w = inverse(w);
for(j = 0; j < size; j += i * 2){
wn = 1;
for(k = 0; k < i; k++){
s = a[j + k], t = mul_(a[j + k + i], wn);
a[j + k] = add_(s, t);
a[j + k + i] = add_(s, MOD_ - t);
wn = mul_(wn, w);
}
}
}
if(rev){
v = inverse(size);
for (i = 0; i < size; i++) a[i] = mul_(a[i], v);
}
}
static void mul(const MPI_& a, const MPI_& b, MPI_& res){
const int size = (int)a.size() + (int)b.size() - 1;
int t = 1;
while (t < size) t <<= 1;
vector<int> A(t, 0), B(t, 0);
for(int i = 0; i < (int)a.size(); i++) A[i] = a[i];
for(int i = 0; i < (int)b.size(); i++) B[i] = b[i];
ntt(A), ntt(B);
for(int i = 0; i < t; i++) A[i] = mul_(A[i], B[i]);
ntt(A, true);
res.resize(size);
int carry = 0;
for(int i = 0; i < size; i++){
int val = A[i] + carry;
carry = val / 10;
res[i] = val % 10;
}
if(carry) res.push_back(carry);
trim_digit(res), trim_sign(res);
}
bool isZero() const {
return (int)size() == 1 && (*this)[0] == 0;
}
static bool div_geq(const MPI_& mod, const MPI_& num){
if((int)mod.size() != (int)num.size()) return (int)mod.size() > (int)num.size();
int n = (int)mod.size();
for(int i = 0; i < n; i++){
if(mod[i] != num[n-1-i]){
return mod[i] > num[n-1-i];
}
}
return true;
}
static void div_(const MPI_& a, const MPI_& b, MPI_& quo, MPI_& mod){
vector<MPI_> mult(9);
mult[0] = b;
for(int i = 0; i < 8; i++) mult[i+1] = mult[i] + b;
for(int i = (int)a.size() - 1; i >= 0; i--){
if(mod.isZero()){
mod.back() = a[i];
}else{
mod.push_back(a[i]);
}
if(div_geq(mod, b)){
int l = 0, r = 9;
reverse(mod.begin(), mod.end());
while(r-l>1){
int mid = (l+r)/2;
if(mult[mid] > mod){
r = mid;
}else{
l = mid;
}
}
mod -= mult[l];
reverse(mod.begin(), mod.end());
quo.push_back(l+1);
}else{
quo.push_back(0);
}
}
reverse(quo.begin(), quo.end());
trim_digit(quo);
reverse(mod.begin(), mod.end());
}
public:
bool sign;
MPI_() : sign(false){ push_back(0); }
MPI_(ll val) : sign(false){
if(val == 0){
push_back(0);
}else{
if(val < 0) sign = true, val = -val;
while(val){
push_back(val%10);
val /= 10;
}
}
}
MPI_(const string& s) : sign(false){
if(s.empty()){
push_back(0);
return;
}
if(s[0] == '-') sign = true;
for(int i = (int)s.size() - 1; i >= sign; i--) push_back(s[i]-'0');
}
ll to_ll() const {
ll res = 0, dig = 1;
for(int i = 0; i < (int)size(); i++){
res += dig * (*this)[i], dig *= 10;
}
if(sign) res = -res;
return res;
}
string to_string() const {
int n = (int)size() + sign;
string s(n, ' ');
if(sign) s[0] = '-';
for(int i = sign; i < n; i++) s[i] = (char)('0'+(*this)[n-1-i]);
return s;
}
friend istream& operator>>(istream& is, MPI_& num) {
string s;
is >> s;
num = MPI_(s);
return is;
}
friend ostream& operator<<(ostream& os, const MPI_& num) {
if(num.sign) os << '-';
for(int i = (int)num.size()-1; i >= 0; i--) os << (char)('0'+num[i]);
return os;
}
MPI_& operator=(ll val) {
*this = MPI_(val);
return *this;
}
bool operator<(const MPI_& another) const {
if(sign ^ another.sign) return sign;
if(size() != another.size()) return (size() < another.size()) ^ sign;
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return ((*this)[index] < another[index]) ^ sign;
}
return false;
}
bool operator<(const ll num) const {
return *this < MPI_(num);
}
friend bool operator<(const ll num, const MPI_& another){
return MPI_(num) < another;
}
bool operator>(const MPI_& another) const {
return another < *this;
}
bool operator>(const ll num) const {
return *this > MPI_(num);
}
friend bool operator>(const ll num, const MPI_& another){
return MPI_(num) > another;
}
bool operator<=(const MPI_& another) const {
return !(*this > another);
}
bool operator<=(const ll num) const {
return *this <= MPI_(num);
}
friend bool operator<=(const ll num, const MPI_& another){
return MPI_(num) <= another;
}
bool operator>=(const MPI_& another) const {
return !(*this < another);
}
bool operator>=(const ll num) const {
return *this >= MPI_(num);
}
friend bool operator>=(const ll num, const MPI_& another){
return MPI_(num) >= another;
}
bool operator==(const MPI_& another) const {
if(sign ^ another.sign) return false;
if(size() != another.size()) return false;
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return false;
}
return true;
}
bool operator==(const ll num) const {
return *this == MPI_(num);
}
friend bool operator==(const ll num, const MPI_& another){
return MPI_(num) == another;
}
bool operator!=(const MPI_& another) const {
return !(*this == another);
}
bool operator!=(const ll num) const {
return *this != MPI_(num);
}
friend bool operator!=(const ll num, const MPI_& another){
return MPI_(num) != another;
}
explicit operator bool() const noexcept { return !isZero(); }
bool operator!() const noexcept { return !static_cast<bool>(*this); }
explicit operator int() const noexcept { return (int)this->to_ll(); }
explicit operator long long() const noexcept { return this->to_ll(); }
MPI_ operator+() const {
return *this;
}
MPI_ operator-() const {
MPI_ res = *this;
res.sign = !sign;
return res;
}
friend MPI_ abs(const MPI_& num){
MPI_ res = num;
res.sign = false;
return res;
}
MPI_ operator+(const MPI_& num) const {
MPI_ res; res.sign = sign;
if(sign != num.sign){
if(abs_less(*this, num)){
res.sign = num.sign;
sub(num, *this, res);
return res;
}else{
sub(*this, num, res);
return res;
}
}
add(*this, num, res);
return res;
}
MPI_ operator+(ll num) const {
return *this + MPI_(num);
}
friend MPI_ operator+(ll a, const MPI_& b){
return b + a;
}
MPI_& operator+=(const MPI_& num){
*this = *this + num;
return *this;
}
MPI_& operator+=(ll num){
*this = *this + num;
return *this;
}
MPI_& operator++(){
return *this += 1;
}
MPI_ operator++(int){
MPI_ res = *this;
*this += 1;
return res;
}
MPI_ operator-(const MPI_& num) const {
if(sign != num.sign){
MPI_ res; res.sign = sign;
add(*this, num, res);
return res;
}
MPI_ res; res.sign = (abs_less(*this, num) ^ sign);
if(res.sign){
sub(num, *this, res);
}else{
sub(*this, num, res);
}
return res;
}
MPI_ operator-(ll num) const {
return *this - MPI_(num);
}
friend MPI_ operator-(ll a, const MPI_& b){
return b - a;
}
MPI_& operator-=(const MPI_& num){
*this = *this - num;
return *this;
}
MPI_& operator-=(ll num){
*this = *this - num;
return *this;
}
MPI_& operator--(){
return *this -= 1;
}
MPI_ operator--(int){
MPI_ res = *this;
*this -= 1;
return res;
}
MPI_ operator*(const MPI_& num) const {
MPI_ res; res.sign = (sign^num.sign);
mul(*this, num, res);
return res;
}
MPI_ operator*(ll num) const {
return *this * MPI_(num);
}
friend MPI_ operator*(ll a, const MPI_& b){
return b * a;
}
MPI_& operator*=(const MPI_& num){
*this = *this * num;
return *this;
}
MPI_& operator*=(ll num){
*this = *this * num;
return *this;
}
MPI_ operator/(const MPI_& num) const {
MPI_ num_ = abs(num);
MPI_ a, b;
div_(*this, num_, a, b);
a.sign = (sign^num.sign);
trim_sign(a);
return a;
}
MPI_ operator/(ll num) const {
return *this / MPI_(num);
}
friend MPI_ operator/(ll a, const MPI_& b){
return b / a;
}
MPI_& operator/=(const MPI_& num){
*this = *this / num;
return *this;
}
MPI_& operator/=(ll num){
*this = *this / num;
return *this;
}
MPI_ operator%(const MPI_& num) const {
MPI_ num_ = abs(num);
MPI_ a, b;
div_(*this, num_, a, b);
b.sign = sign;
trim_sign(b);
return b;
}
MPI_ operator%(ll num) const {
return *this % MPI_(num);
}
friend MPI_ operator%(ll a, const MPI_& b){
return b % a;
}
MPI_& operator%=(const MPI_& num){
*this = *this % num;
return *this;
}
MPI_& operator%=(ll num){
*this = *this % num;
return *this;
}
MPI_ div2() const {
MPI_ res; res.sign = sign;
int n = (int)size(), carry = 0;
for(int i = n-1; i >= 0; i--){
int val = (*this)[i]+carry*10;
carry = val%2;
if(i != n-1 || val >= 2) res.push_back(val/2);
}
reverse(res.begin(), res.end());
trim_digit(res);
return res;
}
friend MPI_ sqrt(const MPI_& x){
if(x <= MPI_(0)) return MPI_(0);
MPI_ s = 1, t = x;
while(s < t){
s = s + s, t = t.div2();
}
do{ t = s, s = (x / s + s).div2();
}while(s < t);
return t;
}
friend MPI_ log10(const MPI_& x){
assert(x > MPI_(0));
return MPI_((int)x.size());
}
friend MPI_ pow(MPI_ a, MPI_ b){
assert(b >= 0);
MPI_ res(1);
while(b){
if(b[0] % 2){
res *= a;
}
a *= a;
b = b.div2();
}
return res;
}
};
template<int acc> class BMPI : public deque<int> {
private:
static constexpr int root = 5;
static constexpr int MOD_ = 924844033;
static void trim_digit(BMPI& num){
while((int)num.size() >= 1 && num.back() == 0) num.pop_back();
if((int)num.size() == 1 && num[0] == 0){ num.zero = true; return; }
while((int)num.size() < acc) num.push_front(0), num.ex--;
while((int)num.size() > acc + 1) num.pop_front(), num.ex++;
rounding(num);
}
static void rounding(BMPI& num){
if((int)num.size() != acc + 1) return;
if(num[0] >= 5){
int pos = 1;
do{ num[pos]++;
if(num[pos] != 10) break;
num[pos] = 0;
}while(++pos <= acc);
if(pos == acc+1) num.push_back(1), num.pop_back(), num.ex++;
}
num.pop_front(), num.ex++;
}
static bool abs_less(const BMPI& a, const BMPI& b){
if(a.ex != b.ex) return a.ex < b.ex;
for(int index = acc - 1; index >= 0; index--){
if(a[index] != b[index]) return a[index] < b[index];
}
return false;
}
static void num_sbst(BMPI& a, const BMPI& b){
a.resize(acc), a.zero = false, a.ex = b.ex;
for(int i = 0; i < acc; i++) a[i] = b[i];
}
static void add(const BMPI& a, const BMPI& b, BMPI& res){
int diff = a.ex - b.ex, carry = 0;
if(abs(diff) > acc) return (diff > 0) ? num_sbst(res, a) : num_sbst(res, b);
if(diff >= 0){
num_sbst(res, a);
if(diff) res.push_front(0), res.ex--;
for(int i = !diff; i <= acc; i++){
int val = res[i-!diff] + (i <= acc-diff ? b[i+diff-1] : 0) + carry;
carry = val/10;
res[i-!diff] = val%10;
}
if(carry) res.push_back(1);
}else{
num_sbst(res, b);
res.push_front(0), res.ex--;
for(int i = 0; i <= acc; i++){
int val = res[i] + (i <= acc+diff ? a[i-diff-1] : 0) + carry;
carry = val/10;
res[i] = val%10;
}
if(carry) res.push_back(1);
}
trim_digit(res);
}
static void sub(const BMPI& a, const BMPI& b, BMPI& res){
int diff = a.ex - b.ex, carry = 0;
num_sbst(res, a);
if(diff > acc) return;
if(diff){
res.push_front(0), res.ex--;
int carry = 0;
for(int i = 0; i <= acc; i++){
int val = res[i] - carry - (i <= acc-diff ? b[i+diff-1] : 0);
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
}else{
for(int i = 0; i < acc; i++){
int val = res[i] - carry - b[i];
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
}
trim_digit(res);
}
static int add_(const int x, const int y) { return (x + y < MOD_) ? x + y : x + y - MOD_; }
static int mul_(const int x, const int y) { return (long long)x * y % MOD_; }
static int power(int x, int n){
int res = 1;
while(n > 0){
if(n & 1) res = mul_(res, x);
x = mul_(x, x);
n >>= 1;
}
return res;
}
static int inverse(const int x) { return power(x, MOD_ - 2); }
static void ntt(vector<int>& a, const bool rev = false){
int i,j,k,s,t,v,w,wn;
const int size = (int)a.size();
const int height = (int)log2(2 * size - 1);
for(i = 0; i < size; i++){
j = 0;
for(k = 0; k < height; k++) j |= (i >> k & 1) << (height - 1 - k);
if(i < j) std::swap(a[i], a[j]);
}
for(i = 1; i < size; i *= 2) {
w = power(root, (MOD_ - 1) / (i * 2));
if(rev) w = inverse(w);
for(j = 0; j < size; j += i * 2){
wn = 1;
for(k = 0; k < i; k++){
s = a[j + k], t = mul_(a[j + k + i], wn);
a[j + k] = add_(s, t);
a[j + k + i] = add_(s, MOD_ - t);
wn = mul_(wn, w);
}
}
}
if(rev){
v = inverse(size);
for (i = 0; i < size; i++) a[i] = mul_(a[i], v);
}
}
static void mul(const BMPI& a, const BMPI& b, BMPI& res){
const int size = (int)a.size() + (int)b.size() - 1;
int t = 1;
while (t < size) t <<= 1;
vector<int> A(t, 0), B(t, 0);
for(int i = 0; i < (int)a.size(); i++) A[i] = a[i];
for(int i = 0; i < (int)b.size(); i++) B[i] = b[i];
ntt(A), ntt(B);
for(int i = 0; i < t; i++) A[i] = mul_(A[i], B[i]);
ntt(A, true);
res.resize(size);
int carry = 0;
for(int i = 0; i < size; i++){
int val = A[i] + carry;
carry = val / 10;
res[i] = val % 10;
}
if(carry) res.push_back(carry);
trim_digit(res);
}
class MPI : public deque<int> {
public:
MPI(){ push_back(0); }
inline static void trim_digit(MPI& num){
while(num.back() == 0 && (int)num.size() >= 2) num.pop_back();
}
bool isZero() const {
return (int)size() == 1 && (*this)[0] == 0;
}
static void add(const MPI& a, const MPI& b, MPI& res){
res = a;
int mx = (int)max(a.size(), b.size());
res.resize(mx, 0);
int carry = 0;
for(int i = 0; i < mx; i++){
int val = res[i] + ((i < (int)b.size()) ? b[i] : 0) + carry;
carry = val/10;
res[i] = val%10;
}
if(carry) res.push_back(1);
}
static void sub(const MPI& a, const MPI& b, MPI& res){
res = a;
int carry = 0;
for(int i = 0; i < (int)res.size(); i++){
int val = res[i] - carry - ((i < (int)b.size()) ? b[i] : 0);
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
trim_digit(res);
}
bool operator<(const MPI& another) const {
if(size() != another.size()) return size() < another.size();
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return (*this)[index] < another[index];
}
return false;
}
static bool div_geq(const MPI& mod, const MPI& num){
if((int)mod.size() != (int)num.size()) return (int)mod.size() > (int)num.size();
int n = (int)mod.size();
for(int i = 0; i < n; i++){
if(mod[n-1-i] != num[n-1-i]){
return mod[n-1-i] > num[n-1-i];
}
}
return true;
}
static void div_(const MPI& a, const MPI& b, MPI& res){
vector<MPI> mult(9);
MPI mod;
mult[0] = b;
for(int i = 0; i < 8; i++) add(mult[i], b, mult[i+1]);
for(int i = (int)a.size() - 1; i >= 0; i--){
if(mod.isZero()){
mod.back() = a[i];
}else{
mod.push_front(a[i]);
}
if(div_geq(mod, b)){
int l = 0, r = 9;
while(r-l>1){
int mid = (l+r)/2;
if(mod < mult[mid]){
r = mid;
}else{
l = mid;
}
}
MPI mod_ = mod;
sub(mod_, mult[l], mod);
res.push_front(l+1);
}else{
res.push_front(0);
}
}
trim_digit(res);
}
};
static void mpi_bmpi(MPI& a, const BMPI& b){
if(b.zero){ a = MPI(0); return; }
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
static void bmpi_mpi(BMPI& a, const MPI& b){
if(b.isZero()){ a = BMPI(); return; }
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
public:
bool sign, zero;
long long ex;
BMPI() : zero(true){}
BMPI(long long val) : sign(false), zero(false), ex(0){
if(val == 0){ zero = true; return; }
if(val < 0) sign = true, val = -val;
while(val) push_back(val%10), val /= 10;
trim_digit(*this);
}
BMPI(const string& s) : sign(false), zero(false), ex(0){
if(s.empty() || s == "0"){ zero = true; return; }
if(s[0] == '-') sign = true;
for(int i = (int)s.size() - 1; i >= sign; i--){
if(s[i] == '.'){
ex = i + 1 - (int)s.size();
}else{
push_back(s[i]-'0');
}
}
trim_digit(*this);
}
friend ostream& operator<<(ostream& os, const BMPI& num) {
if(num.zero){ os << "0."; for(int i = 0; i < acc-1; i++) os << '0';
os << "+e0"; return os; }
if(num.sign) os << '-';
os << num.back() << '.';
for(int i = 0; i < acc-1; i++) os << num[acc-2-i];
os << 'e';
if(num.ex+acc-1 >= 0) os << '+';
os << num.ex+acc-1;
return os;
}
friend istream& operator>>(istream& is, BMPI& num) {
string s;
is >> s;
num = BMPI(s);
return is;
}
void print_decimal(int decimal) const {
if(zero){ cout << "0."; for(int i = 0; i < decimal; i++) cout << '0';}
if(sign) cout << '-';
for(int i = max(ex+acc-1,0LL); i >= -decimal; i--){
cout << ((i-ex >= 0 || i-ex >= acc)?(*this)[i-ex]:'0');
if(i == 0) cout << '.';
}
}
BMPI& operator=(long long num) {
*this = BMPI(num);
return *this;
}
bool operator<(const BMPI& num) const {
if(zero) return !num.zero && !num.sign;
if(num.zero) return sign;
if(sign ^ num.sign) return sign;
if(ex != num.ex) return (ex < num.ex) ^ sign;
for(int index = acc - 1; index >= 0; index--){
if((*this)[index] != num[index]) return ((*this)[index] < num[index]) ^ sign;
}
return false;
}
bool operator<(const long long num) const {
return *this < BMPI(num);
}
friend bool operator<(const long long num, const BMPI& another){
return BMPI(num) < another;
}
bool operator>(const BMPI& num) const {
return num < *this;
}
bool operator>(const long long num) const {
return *this > BMPI(num);
}
friend bool operator>(const long long num, const BMPI& another){
return BMPI(num) > another;
}
bool operator<=(const BMPI& num) const {
return !(*this > num);
}
bool operator<=(const long long num) const {
return *this <= BMPI(num);
}
friend bool operator<=(const long long num, const BMPI& another){
return BMPI(num) <= another;
}
bool operator>=(const BMPI& num) const {
return !(*this < num);
}
bool operator>=(const long long num) const {
return *this >= BMPI(num);
}
friend bool operator>=(const long long num, const BMPI& another){
return BMPI(num) >= another;
}
bool operator==(const BMPI& num) const {
if(zero || num.zero) return zero && num.zero;
if(sign ^ num.sign) return false;
if(ex != num.ex) return false;
for(int index = acc - 1; index >= 0; index--){
if((*this)[index] != num[index]) return false;
}
return true;
}
bool operator==(const long long num) const {
return *this == BMPI(num);
}
friend bool operator==(const long long num, const BMPI& another){
return BMPI(num) == another;
}
bool operator!=(const BMPI& num) const {
return !(*this == num);
}
bool operator!=(const long long num) const {
return *this != BMPI(num);
}
friend bool operator!=(const long long num, const BMPI& another){
return BMPI(num) != another;
}
explicit operator bool() const noexcept { return !zero; }
bool operator!() const noexcept { return !static_cast<bool>(*this); }
explicit operator int() const noexcept { return (int)this->to_ll(); }
explicit operator long long() const noexcept { return this->to_ll(); }
BMPI operator+() const {
return *this;
}
BMPI operator-() const {
BMPI res = *this;
res.sign = !sign;
return res;
}
friend BMPI abs(const BMPI& num){
BMPI res = num;
res.sign = false;
return res;
}
BMPI operator+(const BMPI& num) const {
if(zero){ BMPI res = num; return res; }
if(num.zero){ BMPI res = *this; return res; }
BMPI res; res.sign = sign;
if(sign != num.sign){
if(abs_less(*this, num)){
res.sign = num.sign;
sub(num, *this, res);
return res;
}else{
sub(*this, num, res);
return res;
}
}
add(*this, num, res);
return res;
}
BMPI operator+(long long num) const {
return *this + BMPI(num);
}
friend BMPI operator+(long long a, const BMPI& b){
return b + a;
}
BMPI& operator+=(const BMPI& num){
*this = *this + num;
return *this;
}
BMPI& operator+=(long long num){
*this = *this + num;
return *this;
}
BMPI& operator++(){
return *this += 1;
}
BMPI operator++(int){
BMPI res = *this;
*this += 1;
return res;
}
BMPI operator-(const BMPI& num) const {
if(zero){ BMPI res = num; res.sign = !res.sign; return res; }
if(num.zero){ BMPI res = *this; return res; }
if(sign != num.sign){
BMPI res; res.sign = sign;
add(*this, num, res);
return res;
}
BMPI res; res.sign = (abs_less(*this, num) ^ sign);
if(res.sign){
sub(num, *this, res);
}else{
sub(*this, num, res);
}
return res;
}
BMPI operator-(long long num) const {
return *this - BMPI(num);
}
friend BMPI operator-(long long a, const BMPI& b){
return b - a;
}
BMPI& operator-=(const BMPI& num){
*this = *this - num;
return *this;
}
BMPI& operator-=(long long num){
*this = *this - num;
return *this;
}
BMPI& operator--(){
return *this -= 1;
}
BMPI operator--(int){
BMPI res = *this;
*this -= 1;
return res;
}
BMPI operator*(const BMPI& num) const {
if(zero || num.zero) return BMPI();
BMPI res; res.zero = false; res.sign = (sign^num.sign);
res.ex = ex + num.ex;
mul(*this, num, res);
return res;
}
BMPI operator*(long long num) const {
return *this * BMPI(num);
}
friend BMPI operator*(long long a, const BMPI& b){
return b * a;
}
BMPI& operator*=(const BMPI& num){
*this = *this * num;
return *this;
}
BMPI& operator*=(long long num){
*this = *this * num;
return *this;
}
BMPI operator/(const BMPI& num) const {
assert(!num.zero);
if(zero){ return BMPI(); }
MPI kp, res_, num_;
mpi_bmpi(num_, num);
BMPI res; res.zero = false; res.sign = (sign^num.sign); res.ex = ex - num.ex;
mpi_bmpi(kp, *this);
if(abs_less(*this, num)) kp.push_front(0), res.ex--;
for(int i = 0; i < acc; i++) kp.push_front(0), res.ex--;
MPI::div_(kp, num_, res_);
bmpi_mpi(res, res_);
trim_digit(res);
return res;
}
BMPI operator/(long long num) const {
return *this / BMPI(num);
}
friend BMPI operator/(long long a, const BMPI& b){
return b / a;
}
BMPI& operator/=(const BMPI& num){
*this = *this / num;
return *this;
}
BMPI& operator/=(long long num){
*this = *this / num;
return *this;
}
BMPI div2() const {
if(zero) return BMPI();
BMPI res = *this;
int carry = 0;
for(int i = acc-1; i >= 0; i--){
int val = (*this)[i]+carry*10;
carry = val%2;
if(i != acc-1 || val >= 2){
res[i] = val/2;
}else{
res[i] = 0;
}
}
if(carry) res.push_front(5), res.ex--;
trim_digit(res);
return res;
}
friend BMPI sqrt(BMPI x){
if(x <= BMPI(0)) return BMPI();
BMPI s = 1, t = x;
while(s < t){
s = s + s, t = t.div2();
}
do{ t = s, s = (x / s + s).div2();
}while(s < t);
trim_digit(t);
return t;
}
friend BMPI log10(const BMPI& x){
assert(x > BMPI(0));
return BMPI(acc + x.ex);
}
friend BMPI pow(BMPI a, MPI_ b){
if(a.zero) return BMPI();
assert(!b.sign);
BMPI res(1);
while(b){
if(b[0] % 2) res *= a;
a *= a;
b = b.div2();
}
return res;
}
};
const int ACC = 50;
int main()
{
cin.tie(0);
ios::sync_with_stdio(false);
int n;
cin >> n;
rep(i,n){
BMPI<ACC> x;
MPI_ y;
cin >> x >> y;
BMPI<ACC> z = pow(x,y);
cout << z[ACC-1] << " " << z[ACC-2] << " " << z.ex+ACC-1 << "\n";
}
return 0;
}