new file: AT_agc013_e.cpp

2026-09-16 19:39:01 +08:00
parent 97ce969ae3
commit 67f1f4d5cc
2 changed files with 364 additions and 0 deletions
@@ -0,0 +1,98 @@
+#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;
+}