Added pow

Author: Chillee

content/numerical/FFTPolynomial.h

@@ -12,20 +12,26 @@
 typedef Mod num;
 typedef vector<num> poly;
 vector<Mod> conv(vector<Mod> a, vector<Mod> b) {
-    auto res = convMod<mod>(vl(all(a)), vl(all(b)));
+    // auto res = convMod<mod>(vl(all(a)), vl(all(b)));
+    auto res = conv(vl(all(a)), vl(all(b)));
     return vector<Mod>(all(res));
 }
-poly &operator+=(poly &a, poly &b) {
+poly &operator+=(poly &a, const poly &b) {
     a.resize(max(sz(a), sz(b)));
-    rep(i,0,sz(b)) a[i] = a[i] + b[i];
+    rep(i, 0, sz(b)) a[i] = a[i] + b[i];
     return a;
 }
-poly &operator-=(poly &a, poly b) {
+poly &operator-=(poly &a, const poly &b) {
     a.resize(max(sz(a), sz(b)));
-    rep(i,0,sz(b)) a[i] = a[i] - b[i];
+    rep(i, 0, sz(b)) a[i] = a[i] - b[i];
     return a;
 }
-poly &operator*=(poly &a, poly &b) { return a = conv(a, b); }
+poly &operator*=(poly &a, const poly &b) { return a = conv(a, b); }
+poly operator*(poly a, const num b) {
+    poly c = a;
+    trav(i, c) i = i * b;
+    return c;
+}
 #define OP(o, oe) \
     poly operator o(poly a, poly b) { \
         poly c = a; \
@@ -39,13 +45,13 @@ poly inverse(poly A) {
         B = modK(B * (poly({num(2)}) - A * B), 2 * sz(B));
     return modK(B, sz(A));
 }
-poly &operator/=(poly &a, poly &b) {
+poly &operator/=(poly &a, poly b) {
     if (sz(a) < sz(b))
         return a = {};
     int s = sz(a) - sz(b) + 1;
     reverse(all(a)), reverse(all(b));
     a.resize(s), b.resize(s);
-    a *= inverse(b);
+    a = a * inverse(b);
     a.resize(s), reverse(all(a));
     return a;
 }
@@ -70,7 +76,7 @@ poly integr(poly a) {
     if (a.empty())
         return {0};
     poly b(sz(a) + 1);
-    rep(i,1,sz(b)) b[i] = a[i - 1] / num(i);
+    rep(i, 1, sz(b)) b[i] = a[i - 1] / num(i);
     return b;
 }
 poly log(poly a) { return modK(integr(deriv(a) * inverse(a)), sz(a)); }
@@ -79,9 +85,21 @@ poly exp(poly a) {
     if (a.empty())
         return b;
     while (sz(b) < sz(a)) {
-        b.resize(sz(b)*2);
+        b.resize(sz(b) * 2);
         b *= (poly({num(1)}) + modK(a, sz(b)) - log(b));
-        b.resize(sz(b)/2 + 1);
+        b.resize(sz(b) / 2 + 1);
     }
     return modK(b, sz(a));
 }
+poly pow(poly a, ll m) {
+    int p = 0; int n = sz(a);
+    while (p < sz(a) && a[p].x == 0)
+        ++p;
+    num j = a[p];
+    a = {a.begin() + p, a.end()};
+    a = a * (num(1) / j);
+    a.resize(n);
+    auto res =  exp(log(a) * num(m)) * (j ^ m);
+    res.insert(res.begin(), p*m, 0);
+    return modK(res, n);
+}