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157 lines (132 loc) · 4.47 KB
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package math;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
public final class nCr {
private static class Combinations {
long[] factorial;
long[] facInverse;
long[] inverse;
Combinations(int n) {
final int MAX = n + 2;
factorial = new long[MAX];
facInverse = new long[MAX];
inverse = new long[MAX];
factorial[0] = factorial[1] = 1;
facInverse[0] = facInverse[1] = 1;
inverse[1] = 1;
for (int i = 2; i < MAX; i++) {
factorial[i] = factorial[i - 1] * i % MOD;
final long inv = inverse[i] = MOD - inverse[MOD % i] * (MOD / i) % MOD;
facInverse[i] = facInverse[i - 1] * inv % MOD;
}
}
long ncr(int n, int r) {
if (n < r) { return 0; }
if (n < 0 || r < 0) { return 0; }
return factorial[n] * (facInverse[r] * facInverse[n - r] % MOD) % MOD;
}
long modpow(long a, long n) {
long res = 1;
while (n > 0) {
if (n % 2 == 1) {
res = res * a % MOD;
}
a = a * a % MOD;
n /= 2;
}
return res;
}
}
private static final int MOD = (int) (1e9 + 7);
// TODO https://stackoverflow.com/questions/13146654/calculated-ncr-mod-m-n-choose-r-for-large-values-of-n-109/13211860
public static void main(String[] args) {
final FastScanner fs = new FastScanner();
final Combinations combinations = new Combinations((int) (1e5 + 5));
final long inverse = modInverse(bezout(MOD, 142857)[0], 142857);
final int t = fs.nextInt();
for (int test = 0; test < t; test++) {
System.out.println((combinations.ncr(fs.nextInt(), fs.nextInt()) * inverse) % 142857);
}
}
private static long[] bezout(long a, long b) {
if (b == 0) {
return new long[] { 1, 0 };
}
final long[] res = bezout(b, a % b);
return new long[] { res[1], res[0] - a / b * res[1] };
}
private static long modInverse(long res, long mod) {
return Math.floorMod(res, mod);
}
static final class Utils {
public static void shuffleSort(int[] x) {
shuffle(x);
Arrays.sort(x);
}
public static void shuffleSort(long[] x) {
shuffle(x);
Arrays.sort(x);
}
public static void shuffle(int[] x) {
final Random r = new Random();
for (int i = 0; i <= x.length - 2; i++) {
final int j = i + r.nextInt(x.length - i);
swap(x, i, j);
}
}
public static void shuffle(long[] x) {
final Random r = new Random();
for (int i = 0; i <= x.length - 2; i++) {
final int j = i + r.nextInt(x.length - i);
swap(x, i, j);
}
}
public static void swap(int[] x, int i, int j) {
final int t = x[i];
x[i] = x[j];
x[j] = t;
}
public static void swap(long[] x, int i, int j) {
final long t = x[i];
x[i] = x[j];
x[j] = t;
}
private Utils() {}
}
static class FastScanner {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
StringTokenizer st = new StringTokenizer("");
private String next() {
while (!st.hasMoreTokens()) {
try {
st = new StringTokenizer(br.readLine());
} catch (IOException e) {
//noinspection CallToPrintStackTrace
e.printStackTrace();
}
}
return st.nextToken();
}
int nextInt() {
return Integer.parseInt(next());
}
long nextLong() {
return Long.parseLong(next());
}
int[] nextIntArray(int n) {
final int[] a = new int[n];
for (int i = 0; i < n; i++) { a[i] = nextInt(); }
return a;
}
long[] nextLongArray(int n) {
final long[] a = new long[n];
for (int i = 0; i < n; i++) { a[i] = nextLong(); }
return a;
}
}
}