コード
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
public class Main {
private final int MOD = (int) (1e9 + 7);
private final Combination combination = new Combination(400001, MOD);
private void solve(FastScanner in, PrintWriter out) {
int N = in.nextInt();
int K = in.nextInt();
long[] X = new long[N * 2];
long[] Y = new long[N * 2];
for (int i = 0; i < N; i++) {
X[i] = in.nextInt();
Y[i] = in.nextInt();
}
int px = in.nextInt();
int py = in.nextInt();
for (int i = 0; i < N; i++) {
X[i] -= px;
Y[i] -= py;
X[i + N] = X[i];
Y[i + N] = Y[i];
}
long ans = combination.get(N, K);
int right = 0;
for (int left = 0; left < N; left++) {
right = Math.max(right, left + 1);
while (right < left + N && X[left] * Y[right] - Y[left] * X[right] >= 0) {
right++;
}
ans += MOD - combination.get(right - left - 1, K - 1);
ans %= MOD;
}
out.println(ans % MOD);
}
class Combination {
private long[] fact;
private long[] invFact;
private int MOD;
public Combination(int max, int MOD) {
this.MOD = MOD;
long[] inv = new long[max + 1];
fact = new long[max + 1];
invFact = new long[max + 1];
inv[1] = 1;
for (int i = 2; i <= max; i++) {
inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
}
fact[0] = invFact[0] = 1;
for (int i = 1; i <= max; i++) {
fact[i] = fact[i - 1] * i % MOD;
}
for (int i = 1; i <= max; i++) {
invFact[i] = invFact[i - 1] * inv[i] % MOD;
}
}
public long get(int x, int y) {
if (x < y || y < 0) {
return 0;
}
return fact[x] * invFact[y] % MOD * invFact[x - y] % MOD;
}
}
public static void main(String[] args) {
PrintWriter out = new PrintWriter(System.out);
new Main().solve(new FastScanner(), out);
out.close();
}
private static class FastScanner {
private final InputStream in = System.in;
private final byte[] buffer = new byte[1024];
private int ptr = 0;
private int bufferLength = 0;
private boolean hasNextByte() {
if (ptr < bufferLength) {
return true;
} else {
ptr = 0;
try {
bufferLength = in.read(buffer);
} catch (IOException e) {
e.printStackTrace();
}
if (bufferLength <= 0) {
return false;
}
}
return true;
}
private int readByte() {
if (hasNextByte()) {
return buffer[ptr++];
} else {
return -1;
}
}
private static boolean isPrintableChar(int c) {
return 33 <= c && c <= 126;
}
private void skipUnprintable() {
while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
ptr++;
}
}
boolean hasNext() {
skipUnprintable();
return hasNextByte();
}
public String next() {
if (!hasNext()) {
throw new NoSuchElementException();
}
StringBuilder sb = new StringBuilder();
int b = readByte();
while (isPrintableChar(b)) {
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
long nextLong() {
if (!hasNext()) {
throw new NoSuchElementException();
}
long n = 0;
boolean minus = false;
int b = readByte();
if (b == '-') {
minus = true;
b = readByte();
}
if (b < '0' || '9' < b) {
throw new NumberFormatException();
}
while (true) {
if ('0' <= b && b <= '9') {
n *= 10;
n += b - '0';
} else if (b == -1 || !isPrintableChar(b)) {
return minus ? -n : n;
} else {
throw new NumberFormatException();
}
b = readByte();
}
}
double nextDouble() {
return Double.parseDouble(next());
}
double[] nextDoubleArray(int n) {
double[] array = new double[n];
for (int i = 0; i < n; i++) {
array[i] = nextDouble();
}
return array;
}
double[][] nextDoubleMap(int n, int m) {
double[][] map = new double[n][];
for (int i = 0; i < n; i++) {
map[i] = nextDoubleArray(m);
}
return map;
}
public int nextInt() {
return (int) nextLong();
}
public int[] nextIntArray(int n) {
int[] array = new int[n];
for (int i = 0; i < n; i++) {
array[i] = nextInt();
}
return array;
}
public long[] nextLongArray(int n) {
long[] array = new long[n];
for (int i = 0; i < n; i++) {
array[i] = nextLong();
}
return array;
}
public String[] nextStringArray(int n) {
String[] array = new String[n];
for (int i = 0; i < n; i++) {
array[i] = next();
}
return array;
}
public char[][] nextCharMap(int n) {
char[][] array = new char[n][];
for (int i = 0; i < n; i++) {
array[i] = next().toCharArray();
}
return array;
}
public int[][] nextIntMap(int n, int m) {
int[][] map = new int[n][];
for (int i = 0; i < n; i++) {
map[i] = nextIntArray(m);
}
return map;
}
}
}