Files
luogu/AT_agc013_e.cpp

98 lines
2.4 KiB
C++

#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
int n, m;
int a[100005];
const long long fir[4][2] = {{0, 0}, {0, 1}, {0, 2}, {0, 1}};
const long long yes[4][4] = {{0, 0, 0, 0}, {0, 1, 0, 0}, {0, 2, 1, 0}, {0, 1, 1, 1}};
const long long no[4][4] = {{0, 0, 0, 0}, {0, 1, 0, 1}, {0, 2, 1, 2}, {0, 1, 1, 2}};
struct Mat
{
long long a[5][5] = {};
int n, m;
Mat(int _n = 0, int _m = 0, int cpy = 0) : n(_n), m(_m)
{
if (cpy == 1)
for (int i = 1; i <= 3; ++i)
a[i][1] = fir[i][1];
else if (cpy == 2)
for (int i = 1; i <= 3; ++i)
for (int j = 1; j <= 3; ++j)
a[i][j] = yes[i][j];
else if (cpy == 3)
for (int i = 1; i <= 3; ++i)
for (int j = 1; j <= 3; ++j)
a[i][j] = no[i][j];
}
void operator*=(const Mat &b)
{
if (m != b.n)
exit(-1);
long long res[5][5] = {};
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= b.m; ++j)
for (int k = 1; k <= m; ++k)
res[i][j] = (res[i][j] + a[i][k] * b.a[k][j]) % mod;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= b.m; ++j)
a[i][j] = res[i][j];
m = b.m;
}
Mat operator*(const Mat &b)
{
if (m != b.n)
exit(-1);
Mat res(n, b.m);
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= b.m; ++j)
for (int k = 1; k <= m; ++k)
res.a[i][j] = (res.a[i][j] + a[i][k] * b.a[k][j]) % mod;
return res;
}
};
Mat qpow(Mat a, long long k)
{
Mat res(a.n, a.n);
for (int i = 1; i <= a.n; ++i)
res.a[i][i] = 1;
while (k)
{
if (k & 1)
res *= a;
a *= a;
k >>= 1;
}
return res;
}
Mat yess(3, 3, 2);
Mat noo(3, 3, 3);
int main()
{
scanf("%d%d", &n, &m);
for (int i = 1; i <= m; ++i)
scanf("%d", &a[i]);
Mat now(3, 1, 1);
int pos = 1;
for (int i = 1; i <= m; ++i)
{
int x = a[i];
if (x < pos)
continue;
if (x > pos)
{
now = qpow(noo, x - pos) * now;
}
{
now = yess * now;
}
pos = x + 1;
}
if (n - pos > 0)
{
now = qpow(noo, n - pos) * now;
}
printf("%lld\n", now.a[3][1]);
return 0;
}