Problem: Suppose that P1 is an infinite-height prism whose axis is parallel to the z-axis, and P2 is also an infinite-height prism whose axis is parallel to the y-axis. P1 is defined by the polygon C1 which is the cross section of P1 and the xy-plane, and P2 is also defined by the polygon C2 which is the cross section of P2 and the xz-plane.

Figure I.1 shows two cross sections which appear as the first dataset in the sample input, and Figure I.2 shows the relationship between the prisms and their cross sections.

<image>


Figure I.1: Cross sections of Prisms

<image>


Figure I.2: Prisms and their cross sections

<image>


Figure I.3: Intersection of two prisms

Figure I.3 shows the intersection of two prisms in Figure I.2, namely, P1 and P2.

Write a program which calculates the volume of the intersection of two prisms.



Input

The input is a sequence of datasets. The number of datasets is less than 200.

Each dataset is formatted as follows.

m n
x11 y11
x12 y12
.
.
.
x1m y1m
x21 z21
x22 z22
.
.
.
x2n z2n


m and n are integers (3 ≤ m ≤ 100, 3 ≤ n ≤ 100) which represent the numbers of the vertices of the polygons, C1 and C2, respectively.

x1i, y1i, x2j and z2j are integers between -100 and 100, inclusive. (x1i, y1i) and (x2j , z2j) mean the i-th and j-th vertices' positions of C1 and C2 respectively.

The sequences of these vertex positions are given in the counterclockwise order either on the xy-plane or the xz-plane as in Figure I.1.

You may assume that all the polygons are convex, that is, all the interior angles of the polygons are less than 180 degrees. You may also assume that all the polygons are simple, that is, each polygon's boundary does not cross nor touch itself.

The end of the input is indicated by a line containing two zeros.

Output

For each dataset, output the volume of the intersection of the two prisms, P1 and P2, with a decimal representation in a line.

None of the output values may have an error greater than 0.001. The output should not contain any other extra characters.

Example

Input

4 3
7 2
3 3
0 2
3 1
4 2
0 1
8 1
4 4
30 2
30 12
2 12
2 2
15 2
30 8
13 14
2 8
8 5
13 5
21 7
21 9
18 15
11 15
6 10
6 8
8 5
10 12
5 9
15 6
20 10
18 12
3 3
5 5
10 3
10 10
20 8
10 15
10 8
4 4
-98 99
-99 -99
99 -98
99 97
-99 99
-98 -98
99 -99
96 99
0 0


Output

4.708333333333333
1680.0000000000005
491.1500000000007
0.0
7600258.4847715655

Solution (in CPP):

Solution:
#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 each(a, b) for(auto (a): (b))
#define all(v) (v).begin(),(v).end()
#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 svec(v) cout<<#v<<":";rep(kbrni,v.size())cout<<" "<<v[kbrni];cout<<endl
#define sset(s) cout<<#s<<":";each(kbrni,s)cout <<" "<<kbrni;cout<<endl

using namespace std;

typedef complex<double> C;
typedef pair<int,int>P;

namespace std
{
    bool operator < (const C a, const C b) {
        return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();
    }
}

struct L : public vector<C>
{
    L(const C a, const C b) {
        push_back(a); push_back(b);
    }
};

bool eq(double a,double b)
{
  return (-EPS<a-b&&a-b<EPS);
}

bool eq(C c1,C c2)
{
  return (eq(c1.real(),c2.real()) && eq(c1.imag(),c2.imag()));
}

//?????¶??????sqrt
double Sqrt(double x)
{
    if(x<0) return 0;
    else    return sqrt(x);
}

//??£??????
C normalize(C c)
{
    return c / abs(c);
}

//?§????(rad)
double getarg(C a,C b){
    return  arg(b*conj(a));
}

//??????
double cross(const C a, const C b)
{
    return  imag(conj(a)*b);
}
//??????
double dot(const C a, const C b)
{
    return  real(conj(a)*b);
}

int ccw(C a, C b, C c)
{
    b -= a; c -= a;
    if (cross(b, c) > 0)   return +1;       // counter clockwise
    if (cross(b, c) < 0)   return -1;       // clockwise
    if (dot(b, c) < 0)     return +2;       // c--a--b on line
    if (norm(b) < norm(c)) return -2;       // a--b--c on line
    return 0;
}
//??´???????????????????????????(????????´??????True)
bool intersectLL(const L &l, const L &m)
{
    return abs(cross(l[1]-l[0], m[1]-m[0])) > EPS || abs(cross(l[1]-l[0], m[0]-l[0])) < EPS;
}
//??´?????¨?????????????????????(????????±??????????????¨??????)
bool intersectLS(const L &l, const L &s)
{
    return cross(l[1]-l[0], s[0]-l[0]) * cross(l[1]-l[0], s[1]-l[0]) < EPS;
}
//??´?????¨????????????(??±???)??????
bool intersectLP(const L &l, const C p)
{
    return abs(cross(l[1]-p, l[0]-p)) < EPS;
}
//??????????????????????????????(????????±??????????????¨??????)
bool intersectSS(const L &s, const L &t)
{
    return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 && ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}
//????????¨????????????(??±???)??????
bool intersectSP(const L &s, const C p)
{
    return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS;
}
//???p?????´???l???????°???±
C projection(const L &l, const C p)
{
    double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);
    return l[0] + t*(l[0]-l[1]);
}
//???p?????´???l????????¨??????????§°?§????
C reflection(const L &l, const C p)
{
    return p + (projection(l, p) - p)*2.0;
}
//?????¨??´???????????¢
double distanceLP(const L &l, const C p)
{
    return abs(p - projection(l, p));
}
//??´?????¨??´???????????¢
double distanceLL(const L &l, const L &m)
{
    return intersectLL(l, m) ? 0 : distanceLP(l, m[0]);
}
//??´?????¨??????????????¢
double distanceLS(const L &l, const L &s)
{
    if (intersectLS(l, s)) return 0;
    return min(distanceLP(l, s[0]), distanceLP(l, s[1]));
}
//????????¨???????????¢
double distanceSP(const L &s, const C p)
{
    const C r = projection(s, p);
    if (intersectSP(s, r)) return abs(r - p);
    return min(abs(s[0] - p), abs(s[1] - p));
}
//????????¨??????????????¢
double distanceSS(const L &s, const L &t)
{
    if (intersectSS(s, t)) return 0;
    return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
//??´???????????????????????????
C crosspointLL(const L &l, const L &m)
{
    double A = cross(l[1] - l[0], m[1] - m[0]);
    double B = cross(l[1] - l[0], l[1] - m[0]);
    //????????´????????¨???
    if(abs(A) < EPS && abs(B) < EPS){
        return m[0];
    }
    return m[0] + B / A * (m[1] - m[0]);
}
//?????¨??´????????????
double gettime(C c1,C c2)
{
  return (dot(c1,c2) < 0 ? -1.0 : 1.0 ) * abs(c2) / abs(c1);
}
//?????¨??´????????????
vector<C> crosspointCL(C c1,double r1,L l)
{
    C a=l[0], b=l[1];
    vector<C> res;
    C base=b-a,  target=projection(L(a,b),c1);
    double length=abs(base), h=abs(c1-target);
    base/=length;
    if(r1+EPS<h)    return res;
    double w=Sqrt(r1*r1-h*h);
    double LL=gettime(normalize(b-a),target-a)-w,RR=LL+w*2.0;
    res.push_back(a+base*LL);
    if(eq(LL,RR))   return res;
    res.push_back(a+base*RR);
    return res;
}
//?????¨???????????????
vector<C> crosspointCS(C c1,double r1,L s)
{
    vector<C> tmp=crosspointCL(c1,r1,s);
    vector<C> res;
    rep(i,tmp.size()){
        if(eq(abs(s[1]-s[0]),abs(s[0]-tmp[i])+abs(s[1]-tmp[i]))){
            res.push_back(tmp[i]);
        }
    }
    return res;
}
//?????????????????????
L crosspointCC(const C c1, const double r1, const C c2, const double r2)
{
  C a = conj(c2-c1), b = (r2*r2-r1*r1-(c2-c1)*conj(c2-c1)), c = r1*r1*(c2-c1);
  C d = b*b-4.0*a*c;
  C z1 = (-b+sqrt(d))/(2.0*a)+c1, z2 = (-b-sqrt(d))/(2.0*a)+c1;
  return L(z1, z2);
}
//?????¨????§???¢?????±?????¨????????¢???
double getarea(C c1,double r1,C a,C b)
{
    C va=c1-a,vb=c1-b;
    double A=abs(va),B=abs(vb);
    double f=cross(va,vb),d=distanceSP(L(a,b),c1),res=0;
    if(eq(f,0.0))   return 0;
    if(A < r1+EPS && B < r1+EPS)    return f*0.5;
    if(d>r1-EPS)    return r1*r1*M_PI*getarg(va,vb)/(2.0*M_PI);
    vector<C> u=crosspointCS(c1,r1,L(a,b));
    u.insert(u.begin(),a),u.push_back(b);
    for(int i=0;i+1<(int)u.size();i++){
        res+=getarea(c1,r1,u[i],u[i+1]);
    }
    return res;
}
double getcrossarea(vector<C> t,C c1,double r1)
{
    int n=t.size();
    if(n<3) return 0;
    double res=0;
    rep(i,n){
      C a=t[i], b=t[(i+1)%n];
      res += getarea(c1,r1,a,b);
    }
    return res;
}
//??????????±???????
vector<C> convex_hull(vector<C> ps)
{
    int n = ps.size(), k = 0;
    sort(ps.begin(), ps.end());
    vector<C> ch(2*n);
    for (int i = 0; i < n; ch[k++] = ps[i++]){
        while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) k--;
    }
    for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--]){
        while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) k--;
    }
    ch.resize(k-1);
    return ch;
}
//?????§??????
bool isconvex(const vector<C> &ps)
{
    rep(i,ps.size()){
        if (ccw(ps[(i+ps.size()-1) % ps.size()],ps[i],ps[(i+1) % ps.size()])) return false;
    }
    return true;
}
//????§???¢?????¢???
double area(const vector<C> &ps)
{
    double A = 0;
    rep(i,ps.size()){
        A += cross(ps[i],ps[(i+1) % ps.size()]);
    }
    return A / 2.0;
}
//???????§???¢?????´?????§???????????????????????´????????¢
vector<C> convex_cut(const vector<C> &ps, const L &l)
{
    vector<C> Q;
    rep(i,ps.size()){
        C A = ps[i], B = ps[(i+1)%ps.size()];
        if (ccw(l[0], l[1], A) != -1) Q.push_back(A);
        if (ccw(l[0], l[1], A)*ccw(l[0], l[1], B) < 0)
            Q.push_back(crosspointLL(L(A, B),l));
    }
    return Q;
}
//??????????§???¢???????????????????????????(0??????????????????,1?????????,2???????????????)
int contains(const vector<C>& ps, const C p)
{
    bool flag = false;
    rep(i,ps.size()) {
        C a = ps[i] - p, b = ps[(i+1)%ps.size()] - p;
        if (imag(a) > imag(b)) swap(a, b);
        if (imag(a) <= 0 && 0 < imag(b)){
            if (cross(a, b) < 0) flag = !flag;
        }
        if (cross(a, b) == 0 && dot(a, b) <= 0) return 1;
  }
  return flag ? 2 : 0;
}
//???????§???¢?????´???????±???????(?????£????????????)
//maxi,maxj?????????????????¨??????
double convex_diameter(const vector<C> &ps)
{
    const int n = ps.size();
    int is = 0, js = 0;
    for (int i = 1; i < n; ++i) {
        if (imag(ps[i]) > imag(ps[is])) is = i;
        if (imag(ps[i]) < imag(ps[js])) js = i;
    }
    double maxd = abs(ps[is]-ps[js]);
    int i, maxi, j, maxj;
    i = maxi = is;
    j = maxj = js;
    do{
        if (cross(ps[(i+1)%ps.size()]-ps[i],ps[(j+1)%ps.size()]-ps[j]) >= 0) j = (j+1) % n;
        else i = (i+1) % n;
        if (abs(ps[i]-ps[j]) > maxd) {
            maxd = abs(ps[i]-ps[j]);
            maxi = i; maxj = j;
        }
    } while (i != is || j != js);
    return maxd;
}

bool compyx(C c1,C c2)
{
    return c1.imag() != c2.imag() ? c1.imag() < c2.imag() : c1.real() < c2.real();
}

//????????????????±???????
double closest_pair(C *a, int n)
{
    if(n<=1) return INF;
    int m=n/2;
    double x=a[m].real();
    double d=min(closest_pair(a,m),closest_pair(a+m,n-m));
    inplace_merge(a,a+m,a+n,compyx);
    vector<C> b;
    rep(i,n){
        if(abs(x-a[i].real())>=d) continue;
        rep(j,b.size()){
            C dp=a[i]-b[b.size()-1-j];
            if(dp.imag()>=d) break;
            d=min(d,abs(dp));
        }
        b.push_back(a[i]);
    }
    return d;
}
double compute_shortest(C *a,int n)
{
    sort(a,a+n);
    return closest_pair(a,n);
}
//2??????????????¢????????????(????????????2??????????????±?????\????????°)
int getstateCC(C c1,double r1,C c2,double r2)
{
    double d=abs(c1-c2);
    if(d>r1+r2+EPS)return 4;
    if(d>r1+r2-EPS)return 3;
    if(d>abs(r1-r2)+EPS)return 2;
    if(d>abs(r1-r2)-EPS)return 1;
    return 0;
}
//?????????????????\???????????????????????\???
C gettangentCP_(C c1,double r1,C p,int flg){
    C base=c1-p;
    double w=Sqrt(norm(base)-r1*r1);
    C s=p+base*C(w,r1 * flg)/norm(base)*w;
    return s;
}
//????????????????????\???
vector<L> gettangentCP(C c1,double r1,C p){
    vector<L> res;
    C s=gettangentCP_(c1,r1,p,1);
    C t=gettangentCP_(c1,r1,p,-1);
    //??????????????¨??????????????´???
    if(eq(s,t)){
        res.push_back(L(s,s+(c1-p)*C(0,1)));
    }else{
        res.push_back(L(p,s));
        res.push_back(L(p,t));
    }
    return res;
}

//2????????±????????\???????±???????
L getintangent(C c1,double r1,C c2,double r2,double flg)
{
    C base=c2-c1;
    double w=r1+r2;
    double h=Sqrt(norm(base)-w*w);
    C k=base*C(w,h*flg)/norm(base);
    return L(c1+k*r1,c2-k*r2);
}
//2????????±????????\???????±???????
L getouttangent(C c1,double r1,C c2,double r2,double flg)
{
    C base=c2-c1;
    double h=r2-r1;
    double w=Sqrt(norm(base)-h*h);
    C k=base*C(w,h*flg)/norm(base)*C(0,flg);
    return L(c1+k*r1,c2+k*r2);
}
//2????????±?????\???????±???????(?????´??????????????????????????????????????\???)
vector<L> gettangentCC(C c1,double r1,C c2,double r2)
{
    vector<L> res;
    double d=abs(c1-c2);
    if(d>r1+r2+EPS)  res.push_back(getintangent(c1,r1,c2,r2,1));
    if(d>r1+r2-EPS)  res.push_back(getintangent(c1,r1,c2,r2,-1));
    if(d>abs(r1-r2)+EPS)    res.push_back(getouttangent(c1,r1,c2,r2,1));
    if(d>abs(r1-r2)-EPS)    res.push_back(getouttangent(c1,r1,c2,r2,-1));
    return res;
}

double width(vector<P> vec,int n,double x)
{
    double lb = INF,ub = -INF;
    rep(i,n){
        L hoge(C(vec[i].fi,vec[i].se),C(vec[(i+1)%n].fi,vec[(i+1)%n].se));
        L cri(C(x,101),C(x,-101));
        if(intersectLS(cri,hoge)){
            C res = crosspointLL(cri,hoge);
            lb = min(lb,res.imag());
            ub = max(ub,res.imag());
        }
    }
    return max(0.0,ub-lb);
}

int main()
{
    while(1){
        int n,m;
        cin >> m >> n;
        if(n == 0 && m == 0){
            break;
        }
        vector<P> v1,v2;
        vector<int> ax;
        rep(i,m){
            int x,y;
            cin >> x >> y;
            v1.pb(P(x,y));
            ax.pb(x);
        }
        rep(i,n){
            int x,y;
            cin >> x >> y;
            v2.pb(P(x,y));
            ax.pb(x);
        }
        sort(all(ax));
        ax.erase(unique(all(ax)),ax.end());
        int mn1 = (*min_element(all(v1))).fi;
        int mx1 = (*max_element(all(v1))).fi;
        int mn2 = (*min_element(all(v2))).fi;
        int mx2 = (*max_element(all(v2))).fi;
        double res = 0.0;
        rep(i,ax.size()-1){
            double a = ax[i],b = ax[i+1],c = (a+b)/2;
            if(mn1 <= c && c <= mx1 && mn2 <= c && c <= mx2){
                double fa = width(v1,m,a) * width(v2,n,a);
                double fb = width(v1,m,b) * width(v2,n,b);
                double fc = width(v1,m,c) * width(v2,n,c);
                res += (b - a) / 6 * (fa + 4*fc + fb);
            }
        }
        printf("%.10f\n",res);
    }
    return 0;
}