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@hamadu
Created February 8, 2017 14:27
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package atcoder.arc.arc068;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class Main {
private static final int MOD = 1000000007;
public static void main(String[] args) {
InputReader in = new InputReader(System.in);
PrintWriter out = new PrintWriter(System.out);
int n = in.nextInt();
int k = in.nextInt();
ncr = new int[2010][2010];
for (int i = 0; i < ncr.length; i++) {
ncr[i][0] = ncr[i][i] = 1;
for (int j = 1 ; j < i; j++) {
ncr[i][j] = (ncr[i-1][j] + ncr[i-1][j-1]);
ncr[i][j] %= MOD;
}
}
long ans = 0;
// 次に処理する数,更新フラグ,保留数
int[][][] dp = new int[2][2][n+1];
dp[n%2][0][0] = 1;
for (int i = n ; i >= 1 ; i--) {
int fr = i%2;
int to = fr^1;
for (int flg = 0; flg <= 1; flg++) {
Arrays.fill(dp[to][flg], 0);
}
int haveProcessedNumbers = n - i;
for (int flg = 0; flg <= 1; flg++) {
for (int j = n ; j >= 0; j--) {
if (dp[fr][flg][j] == 0) {
continue;
}
int base = dp[fr][flg][j];
int currentlyInSequence = haveProcessedNumbers - j;
if (currentlyInSequence == k-1) {
ans = addMOD(ans, dp[fr][flg][j]);
continue;
}
if (flg == 1 && j >= 1) {
dp[fr][flg][j-1] = addMOD(dp[fr][flg][j-1], base);
}
if (i == 1) {
continue;
}
dp[to][1][j] = addMOD(dp[to][1][j], base);
dp[to][0][j+1] = addMOD(dp[to][0][j+1], base);
}
}
}
for (int i = 0 ; i < n-k-1 ; i++) {
ans *= 2;
ans %= MOD;
}
out.println(ans);
out.flush();
}
private static int addMOD(long x, long y) {
long ret = x + y;
return (int)(ret >= MOD ? ret-MOD : ret);
}
static int[][] ncr;
static long comb(int n, int k) {
if (n < 0 || k < 0 || n < k) {
return 0;
}
return ncr[n][k] % MOD;
}
// (以下テンプレにつき略)
}
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