1 /**************************************************************
2 Problem: 2179
3 User: idy002
4 Language: C++
5 Result: Accepted
6 Time:1300 ms
7 Memory:10104 kb
8 ****************************************************************/
9
10 #include <cstdio>
11 #include <cstring>
12 #include <iostream>
13 #include <algorithm>
14 #include <cmath>
15 using namespace std;
16
17 typedef long long dnt;
18
19 const double eps = 1e-10;
20 const double dpi = 2*acos(-1);
21 const int N = (1<<17)+10;
22 const int P = 17;
23
24 struct Plex {
25 double x, y;
26 Plex(){}
27 Plex( double x, double y ):x(x),y(y){}
28 };
29 Plex operator-( const Plex &a ) {
30 return Plex(-a.x,-a.y);
31 }
32 Plex operator+( const Plex &a, const Plex &b ) {
33 return Plex(a.x+b.x,a.y+b.y);
34 }
35 Plex operator-( const Plex &a, const Plex &b ) {
36 return Plex(a.x-b.x,a.y-b.y);
37 }
38 Plex operator*( const Plex &a, const Plex &b ) {
39 return Plex(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
40 }
41
42 int n, p;
43 Plex a[N], b[N], c[N], w[P+1];
44 Plex d[N];
45
46 void init() {
47 for( int p=0,i=1; p<=P; p++,i<<=1 ) {
48 w[p] = Plex(cos(dpi/i),sin(dpi/i));
49 }
50 }
51 void read( Plex a[N] ) {
52 static char buf[N];
53 scanf( "%s", buf );
54 int len = strlen(buf);
55 reverse( buf, buf+len );
56 for( int i=0; buf[i]; i++ )
57 a[i].x = buf[i]-'0';
58 }
59 void print( int n, Plex a[N] ) {
60 static int stk[N], top;
61 for( int i=0; i<n; i++ ) {
62 stk[i] += int(a[i].x+0.49);
63 stk[i+1] += stk[i]/10;
64 stk[i] %= 10;
65 }
66 top = n-1;
67 while( top>=1 && stk[top]==0 ) top--;
68 if( top==0 ) {
69 printf( "0\n" );
70 } else {
71 for( int i=top; i>=0; i-- )
72 printf( "%d", stk[i] );
73 printf( "\n" );
74 }
75 }
76 int reverse( int a ) {
77 int b = 0;
78 for( int i=0; i<p; i++ )
79 if( a&(1<<i) ) b |= 1<<(p-1-i);
80 return b;
81 }
82 void fft( Plex a[N], bool r ) {
83 for( int i=0; i<n; i++ ) {
84 int j=reverse(i);
85 if( i<j ) swap(a[i],a[j]);
86 }
87 for( int p=1; p<=::p; p++ ) {
88 for( int i=0; i<n; i+=(1<<p) ) {
89 Plex wo, wk;
90 int l = 1<<(p-1);
91 if( !r ) wo = w[p];
92 else wo = Plex(w[p].x,-w[p].y);
93 wk = w[0];
94 for( int j=0; j<l; j++,wk=wk*wo ) {
95 Plex lf = a[i+j], rg = a[i+j+l];
96 a[i+j] = lf + wk*rg;
97 a[i+j+l] = lf - wk*rg;
98 }
99 }
100 }
101 if( r ) for( int i=0; i<n; i++ )
102 a[i].x /= n;
103 }
104 int main() {
105 scanf( "%d", &n );
106 read(a);
107 read(b);
108 for( p=0; (1<<p)<n; p++ );
109 p++;
110 n = 1<<p;
111 init();
112 fft(a,0);
113 fft(b,0);
114 for( int i=0; i<n; i++ )
115 c[i] = a[i]*b[i];
116 fft(c,1);
117 print(n,c);
118 }
