#include <bits/stdc++.h>
#define jjl(i, j) jl(a[gid(i)], a[gid(j)])
using namespace std;
typedef long long ll;
namespace fastio {
const int bufl = 1 << 16;
const double base1[16] = { 1,    1e-1, 1e-2,  1e-3,  1e-4,  1e-5,  1e-6,  1e-7,
                           1e-8, 1e-9, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14, 1e-15 };
const double base2[16] = {
    1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15
};
struct IN {
    FILE* IT;
    char ibuf[bufl], *is = ibuf, *it = ibuf;
    IN() { IT = stdin; }
    IN(char* a) { IT = fopen(a, "r"); }
    inline char getChar() {
        if (is == it) {
            it = (is = ibuf) + fread(ibuf, 1, bufl, IT);
            if (is == it)
                return EOF;
        }
        return *is++;
    }
    template <typename Temp>
    inline void getInt(Temp& a) {
        a = 0;
        int b = 0, c = getChar();
        while (c < 48 || c > 57) b ^= (c == 45), c = getChar();
        while (c >= 48 && c <= 57) a = (a << 1) + (a << 3) + c - 48, c = getChar();
        if (b)
            a = -a;
    }
    template <typename Temp>
    inline void getDouble(Temp& a) {
        a = 0;
        int b = 0, c = getChar(), d = 0;
        __int128 e = 0, f = 0;
        while (c < 48 || c > 57) b ^= (c == 45), c = getChar();
        while (c >= 48 && c <= 57) e = (e << 1) + (e << 3) + c - 48, c = getChar();
        if (c == 46) {
            c = getChar();
            while (c >= 48 && c <= 57) d++, f = (f << 1) + (f << 3) + c - 48, c = getChar();
        }
        a = e + base1[d] * f;
        if (b)
            a = -a;
    }
    IN& operator>>(char& a) {
        a = getChar();
        return *this;
    }
    IN& operator>>(char* a) {
        do {
            *a = getChar();
        } while (*a <= 32);
        while (*a > 32) *++a = getChar();
        *a = 0;
        return *this;
    }
    IN& operator>>(string& a) {
        char b = getChar();
        while (b <= 32) b = getChar();
        while (b > 32) a += b, b = getChar();
        return *this;
    }
    IN& operator>>(int& a) {
        getInt(a);
        return *this;
    }
    IN& operator>>(long long& a) {
        getInt(a);
        return *this;
    }
    IN& operator>>(__int128& a) {
        getInt(a);
        return *this;
    }
    IN& operator>>(float& a) {
        getDouble(a);
        return *this;
    }
    IN& operator>>(double& a) {
        getDouble(a);
        return *this;
    }
    IN& operator>>(long double& a) {
        getDouble(a);
        return *this;
    }
};
struct OUT {
    FILE* IT;
    char obuf[bufl], *os = obuf, *ot = obuf + bufl;
    int Eps;
    long double Acc;
    OUT() { IT = stdout, Eps = 6, Acc = 1e-6; }
    OUT(char* a) { IT = fopen(a, "w"), Eps = 6, Acc = 1e-6; }
    inline void ChangEps(int x = 6) { Eps = x; }
    inline void flush() {
        fwrite(obuf, 1, os - obuf, IT);
        os = obuf;
    }
    inline void putChar(int a) {
        *os++ = a;
        if (os == ot)
            flush();
    }
    template <typename Temp>
    inline void putInt(Temp a) {
        if (a < 0) {
            putChar(45);
            a = -a;
        }
        if (a < 10) {
            putChar(a + 48);
            return;
        }
        putInt(a / 10);
        putChar(a % 10 + 48);
    }
    template <typename Temp>
    inline void putDouble(Temp a) {
        if (a < 0) {
            putChar(45);
            a = -a;
        }
        __int128 b = a;
        putInt(b);
        a -= b;
        a *= base2[Eps];
        b = a + Acc;
        putChar(46);
        putInt(b);
    }
    OUT& operator<<(char a) {
        putChar(a);
        return *this;
    }
    OUT& operator<<(char* a) {
        while (*a > 32) putChar(*a++);
        return *this;
    }
    OUT& operator<<(string a) {
        for (auto c : a) putChar(c);
        return *this;
    }
    OUT& operator<<(int a) {
        putInt(a);
        return *this;
    }
    OUT& operator<<(long long a) {
        putInt(a);
        return *this;
    }
    OUT& operator<<(__int128 a) {
        putInt(a);
        return *this;
    }
    OUT& operator<<(float a) {
        putDouble(a);
        return *this;
    }
    OUT& operator<<(double a) {
        putDouble(a);
        return *this;
    }
    OUT& operator<<(long double a) {
        putDouble(a);
        return *this;
    }
    ~OUT() { flush(); }
};
}  // namespace fastio
using fastio::IN;
using fastio::OUT;
struct node {
    double x, y;
} a[105];
int n;
double r;
double jl(node x, node y) { return sqrt((x.x - y.x) * (x.x - y.x) + (x.y - y.y) * (x.y - y.y)); }
double qa(double a, double b, double c) { return acos((b * b + c * c - a * a) / b / c / 2); }
double ans;
int gid(int x) { return (x - 1) % n + 1; }
int main() {
    cin >> n >> r;
    for (int i = 1; i <= n; ++i) {
        cin >> a[i].x >> a[i].y;
    }
    for (int i = 1; i < n; ++i) {
        ans += jjl(i, i + 1) * (qa(r, jjl(i, i + 1), r) + qa(r, jjl(i + 1, i + 2), r) -
                                qa(jjl(i, i + 2), jjl(i, i + 1), jjl(i + 1, i + 2)));
    }
    printf("%.15lf", ans);
    return 0;
}