#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <ctime>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <set>
#include <map>
#include <iostream>
#include <deque>
#include <complex>
#include <string>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <valarray>
#include <unordered_map>
#include <iterator>
#include <assert.h>
using namespace std;
typedef long long int ll;
typedef unsigned int uint;
typedef unsigned char uchar;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

#define REP(i,x) for(int i=0;i<(int)(x);i++)
#define REPS(i,x) for(int i=1;i<=(int)(x);i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RREPS(i,x) for(int i=((int)(x));i>0;i--)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++)
#define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++)
#define ALL(container) (container).begin(), (container).end()
#define RALL(container) (container).rbegin(), (container).rend()
#define SZ(container) ((int)container.size())
#define mp(a,b) make_pair(a, b)
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os;
}
template<class T> ostream& operator<<(ostream &os, const set<T> &t) {
os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}
template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first-t.first, s.second-t.second);}

namespace geom{
#define X real()
#define Y imag()
#define at(i) ((*this)[i])
#define SELF (*this)
	enum {TRUE = 1, FALSE = 0, BORDER = -1};
	typedef int BOOL;
	typedef double R;
	const R INF = 1e8;
	R EPS = 1e-8;
	const R PI = 3.1415926535897932384626;
	inline int sig(const R &x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }
	inline BOOL less(const R &x, const R &y) {return sig(x-y) ? x < y : BORDER;}
	typedef complex<R> P;
	inline R norm(const P &p){return p.X*p.X+p.Y*p.Y;}
	inline R inp(const P& a, const P& b){return (conj(a)*b).X;}
	inline R outp(const P& a, const P& b){return (conj(a)*b).Y;}
	inline P unit(const P& p){return p/abs(p);}
	inline P proj(const P &s, const P &t){return t*inp(s, t)/norm(t);}
	inline int ccw(const P &s, const P &t, const P &p, int adv=0){
		int res = sig(outp(t-s, p-s));
		if(res || !adv) return res;
		if(sig(inp(t-s, p-s)) < 0) return -2;	// p-s-t
		if(sig(inp(s-t, p-t)) < 0) return 2;	// s-t-p
		return 0;								// s-p-t
	}
	
	
	struct L : public vector<P>{	// line
		L(const P &p1, const P &p2){this->push_back(p1);this->push_back(p2);}
		L(){}
		P dir()const {return at(1) - at(0);}
		BOOL online(const P &p)const {return !sig(outp(p-at(0), dir()));}
	};
	struct S : public L{	// segment
		S(const P &p1, const P &p2):L(p1, p2){}
		S(){}
		BOOL online(const P &p)const {
			if(!sig(norm(p - at(0))) || !sig(norm(p - at(1)))) return BORDER;
			// 座標の二乗とEPSの差が大きすぎないように注意
			return !sig(outp(p-at(0), dir())) && inp(p-at(0), dir()) > EPS && inp(p-at(1), -dir()) > -EPS;
			//return !sig(abs(at(0)-p) + abs(at(1) - p) - abs(at(0) - at(1)));
		}
	};
	inline P proj(const P &s, const L &t){return t[0] + proj(s-t[0], t[1]-t[0]);}
	inline P reflect(const P &s, const L &t){return (R)2.*proj(s, t) - s;}
	inline S reflect(const S &s, const L &t){return S(reflect(s[0], t), reflect(s[1], t));}
	BOOL intersect(const S &s, const L &l){
		if(l.online(s[0]) || l.online(s[1])) return BORDER;
		return (sig(outp(l.dir(), s[0]-l[0])) * sig(outp(l.dir(), s[1]-l[0])) <= 0);
	}
	inline P crosspoint(const L &l, const L &m){
		R A = outp(l.dir(), m.dir()), B = outp(l.dir(), l[1] - m[0]);
		if(!sig(abs(A)) && !sig(abs(B))) return m[0]; // same line
		if(abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
		return m[0] + B / A * (m[1] - m[0]);
	}

#undef SELF
#undef at
}

using namespace geom;

int f = 0;
namespace std{
	bool operator<(const P &a, const P &b){return sig(a.X-b.X) ? a.X < b.X : a.Y+EPS < b.Y;}
	bool operator==(const P &a, const P &b){return abs(a-b) < EPS;}
	istream& operator>>(istream &is, P &p){R x,y;is>>x>>y;p=P(x, y);return is;}
}

int n, m;

vi path(S root, const vector<P>& pin){
	vi res;
	if(!sig(root.dir().X)) return res;
	REPS(i, n){
		P cp = crosspoint(root, L(pin[i], pin[i]+P(0, 1)));
		if(root.online(cp) == FALSE) continue;
		if(abs(root[0].X - cp.X) < EPS || abs(root[1].X - cp.X) < EPS) continue;
		res.push_back(pin[i].Y < cp.Y ? i : -i);
	}
	sort(ALL(res), [&](int i, int j){
		return abs(root[0].X - pin[abs(i)].X) < abs(root[0].X - pin[abs(j)].X);
	});
	return res;
}

int main(int argc, char *argv[]){
	ios::sync_with_stdio(false);
	int T = 1;
	while(cin >> m >> n, n){
		vector<P> root(m), pin(n+1);
		REP(i, m){
			cin >> root[i];
			root[i] *= polar((R)1, (R)1);
		}
		pin[0] = root[0];
		REPS(i, n){
			cin >> pin[i];
			pin[i] *= polar((R)1, (R)1);
		}
		sort(pin.begin()+1, pin.end());
		pin.push_back(root.back());
		vector<int> st;
		st.push_back(0);
		REP(i, m-1){
			S s(root[i], root[i+1]);
			vi isc = path(s, pin);
			FOR(it, isc){
				if(st.back() == *it) st.pop_back();
				else st.push_back(*it);
			}
		}
		st.push_back(n+1);
		
		vector<R> dp(st.size(), INF);
		dp[0] = .0;
		int save = 0;
		REP(i, st.size()){
			if(i && st[i] == -st[i-1]){
				save = i;
				dp[i] = dp[i-1];
				continue;
			}
			for(int j=save;j<i;j++){
				S r(pin[abs(st[j])], pin[abs(st[i])]);
				vi pt = path(r, pin);
				if([&](){
					for(int k=1;k<=pt.size()&&j+k<i;k++) if(pt[k-1] != st[j+k]) return 0;
					return 1;
				}()) chmin(dp[i], dp[j] + abs(r.dir()));
			}
		}
		printf("%.10f\n", (double)dp.back());
	}
	return 0;
}

Measured memory_bytes: 1376