int
main()
{
int x(0);
int y(0);
int d = extgcd(A, B, x, y);
if (d == 1) {
if (0 <= x) {
std::printf("%d * %d + ", A, x);
}
else {
std::printf("%d * (%d) + ", A, x);
}
if (0 <= y) {
std::printf("%d * %d = 1\n", B, y);
}
else {
std::printf("%d * (%d) = 1\n", B, y);
}
}
return 0;
}
pii extgcd(int a, int b){
if(b == 0) return make_pair(1, 0);
else{
int p = a / b;
pii q = extgcd(b, a % b);
return make_pair(q.second, q.first - q.second * p);
}
}
long long extgcd( long long a,long long b,long long &x,long long &y ) {
long long ret=a;
if ( b ) {
ret=extgcd( b,a%b,y,x );
y-=( a/b )*x;
} else x=1LL,y=0LL;
return ret;
}
// @desc mod mでaの逆元を求める
template <class T> T mod_inverse( T a, T m ) {
T x, y;
extgcd( a, m, x, y );
x %= m;
while ( x < 0 )
x += m;
return x;
}
// 拓展欧几里得算法
// 有如下事实
// 1. a*x+b*y=gcd(a, b) ab不同为0，ab为整数，一定存在整数解
// 2. gcd(a, b) = gcd(b, a mod b)
//
// 那么 a*x+b*y=gcd(a, b)=gcd(b, a mod b)=b*x'+(a mod b)*y'
// 即 a*x+b*y = b*x'+(a-(a/b)*b)*y'
// a*x+b*y = a*y'+b*(x'-(a/b)*y')
// => x <- y', y <- (x'-(a/b)*y')
int extgcd(int a, int b, int& x, int& y)
{
if (b == 0) { x = 1; y = 0; return a; };
int gcd = extgcd(b, a % b, x, y);
int t = y;
y = x - (a / b)*y;
x = t;
return gcd;
}
int extgcd(int a, int b, int& x, int& y){
int d = a;
if (b != 0){
d = extgcd(b, a%b, y, x);
y -= (a/b) * x;
} else {
x = 1; y=0;
}
return d;
}
void extgcd(int a,int b){
if(!b){
if(c%a) ok=false; else ok=true,x=c/a; y=0;
g=a>0?a:-a;
return;
}
extgcd(b,a%b);
if(!ok) return;
int t=x; x=y; y=t-a/b*y;
}
int
main()
{
GEN x, y, d, u, v;
pari_init(1000000,2);
printf("x = "); x = gp_read_stream(stdin);
printf("y = "); y = gp_read_stream(stdin);
d = extgcd(x, y, &u, &v);
pari_printf("gcd = %Ps\nu = %Ps\nv = %Ps\n", d, u, v);
pari_close();
return 0;
}
//（x+kb,y-ka）,(x,y)
void extgcd(long long a,long long b,long long *d,long long *x,long long *y)
{
if(!b)
{
*d=a; *x=1; *y=0;
}
else
{
extgcd(b,a%b,d,y,x);
*y-=(*x)*(a/b);
}
}
//https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
int extgcd(int a, int b, int &x, int &y)
{
if (b == 0)
{
x = 1;
y = 0;
return a;
}
int d = extgcd(b, a % b, x, y);
int t = x;
x = y;
y = t - a / b * y;
return d;
}
Int divide(Int a, Int b, Int m) {
Int g = gcd(a, m);
if (b%g != 0)
throw no_solution();
Int x, y;
extgcd(a, m, x, y);
assert(a*x+m*y == gcd(a,m));
Int n = x*b/g;
Int dn = m/g;
n -= n/dn*dn;
if (n < 0)
n += dn;
return n;
}
int main() {
long long a,b,c,k;
while ( ~scanf( "%I64d%I64d%I64d%I64d",&a,&b,&c,&k ) ) {
if ( !a&&!b&&!c&&!k )break;
long long x,y;
long long z=extgcd( c,1LL<<k,x,y );
long long tp=( b-a )/z;
if ( tp*z==( b-a ) ) {
long long t=x;
t*=tp;
long long mod = ( 1LL<<k )/z;
t%=mod;
t+=mod;
t%=mod;
printf( "%I64d\n",t );
} else printf( "FOREVER\n" );
}
return 0;
}
int main (void)
{
int x,y,m,n;
int x1,y1;
int a,b,c;
while(scanf("%d %d %d %d %d",&x,&y,&m,&n,&b)!=EOF)
{
a=m-n;
c=y-x;
int r=extgcd(a,b,x1,y1);
if(c%r)
printf("Impossible\n");
else
{
x1=(c*x1/r)%b;
if(x1<0)x1+=b;
printf("%d\n",x1);
}
}
return 0;
}
int extoclean(int x, int y, int z) {
int ret = extgcd(x, y); int ans;
if (z%ret) return -1;
ans = ((long long)(z/ret)*k1%(y/ret));
if (ans < 0) ans += y/ret; return ans;
}
int mod_inverse(int a, int m) {
int x, y;
extgcd(a, m, x, y);
return (m + x % m) % m;
}
T extgcd(T a, T b, T& x, T& y) {
T g = 1; x = 1; y = 0;
if (b != 0) g = extgcd(b, a % b, y, x), y -= (a / b) * x;
return g;
}
int main()
{
long long p1, v1, p2, v2, l;
long long t, disv, dist, td;
long long temp;
long long a, b, d;
long long x, y;
while(scanf("%lld %lld %lld %lld %lld", &p1, &p2, &v1, &v2, &l) != EOF)
{
while(p1 >= l)
p1 -= l;
while(p2 >= l)
p2 -= l;
if (v1 < v2)
{
temp = v1;
v1 = v2;
v2 = temp;
temp = p1;
p1 = p2;
p2 = temp;
}
if (p1 > p2)
dist = l - p1 + p2;
else
dist = p2 - p1;
disv = v1 - v2;
if (disv == 0)
{
if (dist != 0)
printf("Impossible\n");
else
printf("0\n");
continue;
}
// printf("%lld %lld %lld %lld\n", p1, p2, l, dist);
// disv * x + (-y) * l = dist
if (dist % gcd(disv, l) != 0)
{
printf("Impossible\n");
continue;
}
extgcd(disv, l, &d, &a, &b);
// printf("%lld\n", disv * a - l * b);
// printf("%lld %lld %lld %lld %lld %lld\n",disv, l, a, b, disv * a + l * b, d);
x = a; y = b;
x *= dist / d;
y *= dist / d;
x -= (x / (l / d)) * (l / d);
while (x <= 0)
x += l / d;
printf("%lld\n", x);
}
return 0;
}
T invMod(T a, T mod) {
T x, y;
if (extgcd(a, mod, x, y) == -1) return (x + mod) % mod;
return 0;
}
int mod_inv(int a, int m) {
int x, y;
extgcd(a, m, x, y);
return (m + x) % m;
}
Int invMod(Int a, Int m) {
Int x, y;
if (extgcd(a, m, x, y) == 1) return (x + m) % m;
else return 0; // unsolvable
}
// a x + b y = gcd(a, b)
Int extgcd(Int a, Int b, Int &x, Int &y) {
Int g = a; x = 1; y = 0;
if (b != 0) g = extgcd(b, a % b, y, x), y -= (a / b) * x;
return g;
}
int extgcd(int x, int y) {
int ret, tmp;
if (!y) { k1 = 1; k2 = 0; return x; }
ret = extgcd(y, x%y);
tmp = k1-x/y*k2; k1 = k2; k2 = tmp; return ret;
}
