/*
Colectia personala de operatii pe numere mari - C++ ( classes )
Implementate de Robert Simoiu
Incluzand extragerea radacinii patrate cu oricate zecimale
*/
# include <cmath>
# include <cstdio>
# include <cstring>
# include <vector>
using namespace std ;
/*
precizare :
1. Daca vreti sa faceti a = b + c, in loc de a += b , trebuie in loc de void operator += ( ... )
sa faceti Mare operator + ( ... ) , si sa returnati un vector Mare ( exemplu prima functie, Mare operator + ( Mare& ) )
2. Pentru comparari, se poate face usor > si >=, doar schimband returnurile ( fals cu adevarat, si invers ), dar
e de preferabil ca a > b sa se faca ca si b < a ( pentru a nu mai fi nevoie de introducerea unei noi comparari )
*/
# define MAX 3 // numarul de cifre
# define verf( X, i ) ( i <= X[0] ? X[i] : 0 )
# define A ( *this )
class Mare : protected vector < int > {
protected :
static const int base = 1000000000, nbase = 9 ;
public :
Mare ( ) ;
Mare ( int ) ;
void operator = ( char* ) ;
Mare operator + ( Mare& ) ;
int operator % ( int ) ;
Mare operator % ( Mare& ) ;
void operator += ( Mare& ) ;
void operator *= ( int ) ;
void operator *= ( Mare& ) ;
void operator -= ( Mare& ) ;
bool operator < ( Mare& ) ;
bool operator <= ( Mare& ) ;
void operator <<= ( int ) ;
void operator >>= ( int ) ;
void operator /= ( int ) ;
void operator /= ( Mare& ) ;
void radical_normal ( Mare&, int ) ;
void radical_cb ( Mare& ) ;
void pow ( int ) ;
void afis ( void ) ;
void afis_rad ( int ) ;
void transform_10 ( char* ) ;
void obtain ( int, char* ) ;
int zero ( void ) ;
} ;
Mare :: Mare () { // A = 0
this -> resize ( MAX ) ;
}
Mare :: Mare ( int X ) { // A = X
this -> resize ( MAX ) ;
for ( A[0] = 0; X ; X /= base ) {
A[ ++A[0] ] = X % base ;
}
}
Mare Mare :: operator + ( Mare &B ) { // C = A + B
int i, t = 0;
Mare C ;
for ( i = 1; i <= A[0] || i <= B[0] || t; ++i, t /= base )
C[i] = ( t += verf ( A, i ) + verf ( B, i ) ) % base ;
C[0] = i - 1;
return C ;
}
int Mare :: operator % ( int B ) { // A % B
int i, t = 0;
for (i = A[0]; i ; --i)
t = ( t * base + A[i] ) % B ;
return t ;
}
void Mare :: operator += ( Mare &B ) { // A += B
int i, t = 0;
for ( i = 1; i <= A[0] || i <= B[0] || t; ++i, t /= base )
A[i] = ( t += verf ( A, i ) + verf ( B, i ) ) % base ;
A[0] = i - 1;
}
void Mare :: operator *= ( int B ) { // A *= B
int i = 1;
for ( long long t = 0; i <= A[0] || t; ++i, t /= base )
A[i] = ( t += 1LL * verf ( A, i ) * B ) % base ;
A[0] = i - 1;
}
void Mare :: operator -= ( Mare &B ) { // A -= B, ∀ A ≥ B
int t = 0;
for ( int i = 1; i <= A[0]; ++i ) {
t = ( A[i] -= verf ( B, i ) + t ) < 0 ;
A[i] += t * base ;
}
for ( ; A[0] > 1 && !A[A[0]]; --A[0] ) ;
}
bool Mare :: operator < ( Mare &B ) { // A < B ?
for ( ; A[0] && !A[ A[0] ] ; --A[0] ) ;
for ( ; B[0] && !B[ B[0] ] ; --B[0] ) ;
if ( A[0] < B[0] ) return true;
else if ( A[0] > B[0] ) return false;
for ( int i = A[0]; i > 0; --i )
if ( A[i] < B[i] ) return true;
else if ( A[i] > B[i] ) return false;
return false;
}
bool Mare :: operator <= ( Mare &B ) { // A <= B ?
for ( ; A[0] && !A[ A[0] ] ; --A[0] ) ;
for ( ; B[0] && !B[ B[0] ] ; --B[0] ) ;
if ( A[0] < B[0] ) return true;
else if ( A[0] > B[0] ) return false;
for ( int i = A[0]; i > 0; --i )
if ( A[i] < B[i] ) return true;
else if ( A[i] > B[i] ) return false;
return true;
}
void Mare :: operator *= ( Mare &B ) { // A *= B
Mare C ;
for ( int i = 1, j; i <= A[0]; ++i ) {
long long t = 0 ;
for ( j = 1; j <= B[0] || t; ++j, t /= base)
C[i + j - 1] = ( t += C[i + j - 1] + 1LL * verf ( A, i ) * verf ( B, j ) ) % base;
if ( i + j - 2 > C[0] )
C[0] = i + j - 2;
}
A = C ;
}
void Mare :: operator /= ( int B ) { // A /= B
int t = 0;
for ( int i = A[0]; i > 0; i--, t %= B )
A[i] = ( t = t * base + A[i] ) / B ;
for ( ; A[0] > 1 && !A[ A[0] ]; --A[0] ) ;
}
Mare Mare :: operator % ( Mare &B ) { // A % B
char X[MAX * nbase]; Mare R = 0, T, C;
A.transform_10 ( X ) ;
for ( int i = 1; i <= A[0]; ++i )
C[i] = 0 ;
for ( int i = X[0]; i ; --i ) {
R <<= R.zero () ? 0 : 1, T = X[i], R += T ;
for ( C[i / nbase + ( i % nbase != 0 )] *= 10; B <= R ; ++C[i / nbase + ( i % nbase != 0 )], R -= B ) ;
}
return R ;
}
void Mare :: radical_cb ( Mare &B ) { // B = sqrt ( A ) ; doar parte intreaga
Mare cnt, X ;
for ( cnt = 1; cnt < A; cnt *= 2 ) ;
for ( B[0] = 1 ; ! ( cnt[1] == 0 && cnt[0] == 1 ) ; cnt /= 2 ) {
X = cnt, X += B, X *= X ;
if ( X <= A )
B += cnt ;
}
}
void Mare :: obtain ( int x, char *X ) {
int S[11] = { 0 } ;
for ( int i = A[x]; i ; i /= 10 )
S[ ++S[0] ] = i % 10 ;
for ( int i = 1; i <= S[0] ; ++i )
X[ ++X[0] ] = S[i] ;
if ( x != A[0] )
for ( int i = S[0]; i < nbase; ++i )
X[ ++X[0] ] = 0 ;
}
void Mare :: transform_10 ( char *X ) {
X[0] = 0 ;
for ( int i = 1; i <= A[0]; ++i ) {
obtain ( i, X ) ;
}
}
void Mare :: radical_normal ( Mare &B, int nrzecimale ) {
int AUX = 0, i , j = 0 ; char X[MAX * nbase] ;
Mare C, D, E, F, U ( 9 ), Z ( 1 ) ;
A.transform_10 ( X ), i = X[0] ;
( X[0] & 1 ) ? AUX = X[i--] : ( AUX = X[i--], AUX *= 10, AUX += X[i--] ) ;
int aux = static_cast < int > ( sqrt ( AUX ) ) ;
B = aux ;
if ( X[0] > 2 ) {
AUX -= aux * aux;
E = AUX, E <<= 1, F = X[i--];
if ( AUX ) E += F, E <<= 1 ;
else E = F ;
if ( AUX == 0 && X[i + 1] != 0 ) E <<= 1 ;
F = X[i--], E += F ;
C = E, F = B, F *= 2, E = F ;
D = C, D >>= 1, D /= E ;
if ( U < D ) {
D = 9 ;
}
E <<= 1, E += D, E *= D ;
while ( C < E )
D -= Z, F = B, F *= 2, E = F, E <<= 1, E += D, E *= D ;
C -= E ;
B <<= 1, B += D ;
} else {
C = AUX - ( aux * aux ) ;
}
if ( !C.zero () || i > 0 ) {
for ( i = i; i > 0 || j < nrzecimale ; ) {
if ( i > 0 ) {
E = X[i--], F = 0, F <<= 1, F = E, E = X[i--];
if ( X[i + 2] ) F <<= 1, F += E ;
else F = E ;
} else {
++j, F = 0 ;
if ( j == 1 && C.zero () ) {
for ( int i = 1; i <= nrzecimale ; ++i )
B <<= 1 ;
return ;
}
}
if ( !C.zero () || i == 3 + ( X[0] % 2 == 0 ) && AUX ) {
C <<= 2, C += F ;
} else {
C = F ;
}
F = B, F *= 2, E = F ;
D = C, D >>= 1, D /= E ;
if ( U < D ) {
D = 9 ;
}
E <<= 1, E += D, E *= D ;
while ( C < E )
D -= Z, F = B, F *= 2, E = F, E <<= 1, E += D, E *= D ;
C -= E ;
B <<= 1, B += D ;
}
} else {
for ( int i = 1; i <= nrzecimale ; ++i ) {
B <<= 1 ;
}
}
}
void Mare :: pow ( int P ) {
Mare B = 1 ;
for ( ; P ; P >>= 1 ) {
if ( P & 1 ) {
B *= A ;
}
A *= A ;
}
A = B ;
}
void Mare :: afis ( void ) {
printf ( "%d", A[ A[0] ] ) ;
for ( int i = A[0] - 1; i ; --i ) {
printf ( "%09d", A[i] ) ;
}
}
void Mare :: afis_rad ( int nrzecimale ) { // afisarea radicalului
char X[MAX * nbase] ;
A.transform_10 ( X ) ;
for ( int i = X[0]; i > nrzecimale ; --i )
printf ( "%d", X[i] ) ;
printf ( "." ) ;
for ( int i = nrzecimale ; i ; --i ) {
printf ( "%d", X[i] ) ;
}
}
void Mare :: operator = ( char *X ) {
A[0] = 0;
if ( X ) {
for ( int h = strlen ( X ) ; h > 0 ; h -= nbase ) {
++A[0], A[ A[0] ] = 0 ;
for ( int i = max ( 0, h - nbase ) ; i < h; ++i ) {
A[ A[0] ] = A[ A[0] ] * 10 + X[i] - '0' ;
}
}
}
}
int Mare :: zero ( void ) {
return A[0] == 0 || A[0] == 1 && A[1] == 0 ;
}
void Mare :: operator /= ( Mare &B ) { // A /= B
char X[MAX * nbase];
Mare R = 0, T ;
A.transform_10 ( X ) ;
for ( int i = 1; i <= A[0]; ++i )
A[i] = 0 ;
for ( int i = X[0]; i ; --i ) {
R <<= R.zero () ? 0 : 1, T = X[i], R += T ;
for ( A[i / nbase + ( i % nbase != 0 )] *= 10; B <= R ; ++A[i / nbase + ( i % nbase != 0 )], R -= B ) ;
}
for ( ; !A[ A[0] ] && A[0] > 1 ; --A[0] ) ;
}
void Mare :: operator <<= ( int Count ) { // A *= ( 10^Count )
if ( Count ) {
if ( A.zero () ) A = 1 ;
Mare sol = 10 ;
sol.pow ( Count ), A *= sol ;
}
}
void Mare :: operator >>= ( int Count ) { // A /= ( 10^Count )
if ( Count ) {
Mare sol = 10 ;
sol.pow ( Count ), A /= sol ;
}
}
# undef A
int T ;
Mare X, Y, Z ;
char A[10], B[10] ;
inline void euclid ( Mare A, Mare B, Mare &C ) {
while ( ! B.zero () ) {
Mare R = A % B ;
A = B ;
B = R ;
}
C = A ;
}
int main ( void ) {
freopen ( "euclid2.in", "r", stdin ) ;
freopen ( "euclid2.out", "w", stdout ) ;
for ( scanf ( "%d", &T ) ; T ; --T ) {
scanf ( "%s %s", A, B ) ;
X = A, Y = B ;
euclid ( X, Y, Z ) ;
Z.afis () ; printf ( "\n" ) ;
}
}