add min mod (mimumum of linear function modulo m)

1 files changed, 18 insertions, 0 deletions

diff --git a/content/math/minMod.cpp b/content/math/minMod.cpp
new file mode 100644
index 0000000..2db060a
--- /dev/null
+++ b/content/math/minMod.cpp
@@ -0,0 +1,18 @@
+ll firstVal(ll a, ll m, ll l, ll r){
+	if(l == 0) return 0;
+	if(a == 0) return -1;
+	if((l-1)/a < r/a) return (l+a-1)/a*a;
+	ll s = (r+a-1)/a*a;
+	ll v = firstVal(m%a, a, s-r, s-l);
+	return v == -1 ? -1 : s - v;
+}
+
+ll minMod(ll n, ll m, ll a, ll b){
+	if(a == 0) return b;
+	ll g = gcd(m, a), c = b%g;
+	m /= g, a /= g, b /= g;
+	ll ai = multInv(a, m);
+	ll l = ai*b % m, r = (n-1 + ai*b) % m;
+	if(n >= m || l > r) return c;
+	return a * firstVal(ai, m, l, r) % m * g + c;
+}
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