#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;
}